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Exercícios de sistemas de equações · Physics Playground

ExercíciosMatemática

Sistemas de equações

121 problemas com soluções resolvidas, de Elementary Algebra e Algebra and Trigonometry.

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Elementary Algebra5.1 Solve Systems of Equations by Graphing

Exemplo 5.1Determine whether the ordered pair is a solution to the system: {x−y=−12x−y=−5 ⓐ (−2,−1) ⓑ (−4,−3)Mais um parecido para tentar
Exemplo 5.2Solve the system by graphing: {2x+y=7x−2y=6.Mais um parecido para tentar
Exemplo 5.3Solve the system by graphing: {y=2x+1y=4x−1.Mais um parecido para tentar
Exemplo 5.4Solve the system by graphing: {3x+y=−12x+y=0.Mais um parecido para tentar
Exemplo 5.5Solve the system by graphing: {x+y=2x−y=4.Mais um parecido para tentar
Exemplo 5.6Solve the system by graphing: {y=62x+3y=12.Mais um parecido para tentar
Exemplo 5.7Solve the system by graphing: {y=1/2x−3x−2y=4.Mais um parecido para tentar
Exemplo 5.8Solve the system by graphing: {y=2x−3−6x+3y=−9.Mais um parecido para tentar
Exemplo 5.9Without graphing, determine the number of solutions and then classify the system of equations: {y=3x−16x−2y=12.Mais um parecido para tentar
Exemplo 5.10Without graphing, determine the number of solutions and then classify the system of equations: {2x+y=−3x−5y=5.Mais um parecido para tentar
Exemplo 5.11Without graphing, determine the number of solutions and then classify the system of equations. {3x−2y=4y=3/2x−2Mais um parecido para tentar
Exemplo 5.12Sondra is making 10 quarts of punch from fruit juice and club soda. The number of quarts of fruit juice is 4 times the number of quarts of club soda. How many quarts of fruit juice and how many quarts of club soda…Mais um parecido para tentar

Elementary Algebra5.2 Solve Systems of Equations by Substitution

Exemplo 5.13Solve the system by substitution. {2x+y=7x−2y=6Mais um parecido para tentar
Exemplo 5.14Solve the system by substitution. {x+y=−1y=x+5Mais um parecido para tentar
Exemplo 5.15Solve the system by substitution. {3x+y=52x+4y=−10Mais um parecido para tentar
Exemplo 5.16Solve the system by substitution. {x−2y=−23x+2y=34Mais um parecido para tentar
Exemplo 5.17Solve the system by substitution. {y=−2x+5y=1/2xMais um parecido para tentar
Exemplo 5.18Solve the system by substitution. {4x+2y=46x−y=8Mais um parecido para tentar
Exemplo 5.19Solve the system by substitution. {4x−3y=615y−20x=−30Mais um parecido para tentar
Exemplo 5.20Solve the system by substitution. {5x−2y=−10y=5/2xMais um parecido para tentar
Exemplo 5.21The sum of two numbers is zero. One number is nine less than the other. Find the numbers.Mais um parecido para tentar
Exemplo 5.22The perimeter of a rectangle is 88. The length is five more than twice the width. Find the length and the width.Mais um parecido para tentar
Exemplo 5.23The measure of one of the small angles of a right triangle is ten more than three times the measure of the other small angle. Find the measures of both angles.Mais um parecido para tentar
Exemplo 5.24Heather has been offered two options for her salary as a trainer at the gym. Option A would pay her $25,000 plus $15 for each training session. Option B would pay her $10,000 + $40 for each training session. How many…Mais um parecido para tentar

Elementary Algebra5.3 Solve Systems of Equations by Elimination

Exemplo 5.25Solve the system by elimination. {2x+y=7x−2y=6Mais um parecido para tentar
Exemplo 5.26Solve the system by elimination. {x+y=10x−y=12Mais um parecido para tentar
Exemplo 5.27Solve the system by elimination. {3x−2y=−25x−6y=10Mais um parecido para tentar
Exemplo 5.28Solve the system by elimination. {4x−3y=97x+2y=−6Mais um parecido para tentar
Exemplo 5.29Solve the system by elimination. {x+1/2y=63/2x+2/3y=(17)/2Mais um parecido para tentar
Exemplo 5.30Solve the system by elimination. {3x+4y=12y=3−3/4xMais um parecido para tentar
Exemplo 5.31Solve the system by elimination. {−6x+15y=102x−5y=−5Mais um parecido para tentar
Exemplo 5.32The sum of two numbers is 39. Their difference is 9. Find the numbers.Mais um parecido para tentar
Exemplo 5.33Joe stops at a burger restaurant every day on his way to work. Monday he had one order of medium fries and two small sodas, which had a total of 620 calories. Tuesday he had two orders of medium fries and one small…Mais um parecido para tentar
Exemplo 5.34For each system of linear equations decide whether it would be more convenient to solve it by substitution or elimination. Explain your answer. ⓐ {3x+8y=407x−4y=−32 ⓑ {5x+6y=12y=2/3x−1Mais um parecido para tentar

Elementary Algebra5.4 Solve Applications with Systems of Equations

Exemplo 5.35Translate to a system of equations: The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.Mais um parecido para tentar
Exemplo 5.36Translate to a system of equations: A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?Mais um parecido para tentar
Exemplo 5.37Translate to a system of equations and then solve: Devon is 26 years older than his son Cooper. The sum of their ages is 50. Find their ages.Mais um parecido para tentar
Exemplo 5.38Translate to a system of equations and then solve: When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for 20 minutes, her fitness app says she burned 278 calories. When she spent 20…Mais um parecido para tentar
Exemplo 5.39Translate to a system of equations and then solve: The difference of two complementary angles is 26 degrees. Find the measures of the angles.Mais um parecido para tentar
Exemplo 5.40Translate to a system of equations and then solve: Two angles are supplementary. The measure of the larger angle is twelve degrees less than five times the measure of the smaller angle. Find the measures of both angles.Mais um parecido para tentar
Exemplo 5.41Translate to a system of equations and then solve: Randall has 125 feet of fencing to enclose the rectangular part of his backyard adjacent to his house. He will only need to fence around three sides, because the…Mais um parecido para tentar
Exemplo 5.42Translate to a system of equations and then solve: Joni left St. Louis on the interstate, driving west towards Denver at a speed of 65 miles per hour. Half an hour later, Kelly left St. Louis on the same route as…Mais um parecido para tentar
Exemplo 5.43Translate to a system of equations and then solve: A river cruise ship sailed 60 miles downstream for 4 hours and then took 5 hours sailing upstream to return to the dock. Find the speed of the ship in still water…Mais um parecido para tentar
Exemplo 5.44Translate to a system of equations and then solve: A private jet can fly 1095 miles in three hours with a tailwind but only 987 miles in three hours into a headwind. Find the speed of the jet in still air and the…Mais um parecido para tentar

Elementary Algebra5.5 Solve Mixture Applications with Systems of Equations

Exemplo 5.45Translate to a system of equations and solve: The box office at a movie theater sold 147 tickets for the evening show, and receipts totaled $1,302. How many $11 adult and how many $8 child tickets were sold?Mais um parecido para tentar
Exemplo 5.46Translate to a system of equations and solve: Priam has a collection of nickels and quarters, with a total value of $7.30. The number of nickels is six less than three times the number of quarters. How many nickels…Mais um parecido para tentar
Exemplo 5.47Translate to a system of equations and solve: Carson wants to make 20 pounds of trail mix using nuts and chocolate chips. His budget requires that the trail mix costs him $7.60 per pound. Nuts cost $9.00 per pound…Mais um parecido para tentar
Exemplo 5.48Translate to a system of equations and solve: Sasheena is a lab assistant at her community college. She needs to make 200 milliliters of a 40% solution of sulfuric acid for a lab experiment. The lab has only 25% and…Mais um parecido para tentar
Exemplo 5.49Translate to a system of equations and solve: Adnan has $40,000 to invest and hopes to earn 7.1% interest per year. He will put some of the money into a stock fund that earns 8% per year and the rest into bonds that…Mais um parecido para tentar
Exemplo 5.50Translate to a system of equations and solve: Rosie owes $21,540 on her two student loans. The interest rate on her bank loan is 10.5% and the interest rate on the federal loan is 5.9%. The total amount of interest…Mais um parecido para tentar

Elementary Algebra5.6 Graphing Systems of Linear Inequalities

Exemplo 5.51Determine whether the ordered pair is a solution to the system. {x+4y≥103x−2y<12 ⓐ (−2, 4) ⓑ (3,1)Mais um parecido para tentar
Exemplo 5.52Solve the system by graphing. {y≥2x−1y<x+1Mais um parecido para tentar
Exemplo 5.53Solve the system by graphing. {x−y>3y<−1/5x+4Mais um parecido para tentar
Exemplo 5.54Solve the system by graphing. {x−2y<5y>−4Mais um parecido para tentar
Exemplo 5.55Solve the system by graphing. {4x+3y≥12y<−4/3x+1Mais um parecido para tentar
Exemplo 5.56Solve the system by graphing. {y>1/2x−4x−2y<−4Mais um parecido para tentar
Exemplo 5.57Christy sells her photographs at a booth at a street fair. At the start of the day, she wants to have at least 25 photos to display at her booth. Each small photo she displays costs her $4 and each large photo costs…Mais um parecido para tentar
Exemplo 5.58Omar needs to eat at least 800 calories before going to his team practice. All he wants is hamburgers and cookies, and he doesn’t want to spend more than $5. At the hamburger restaurant near his college, each…Mais um parecido para tentar

Algebra and Trigonometry11.1 Systems of Linear Equations: Two Variables

Exemplo 1Determining Whether an Ordered Pair Is a Solution to a System of EquationsDetermine whether the ordered pair ( 5,1) is a solution to the given system of equations. x+3y=8 2x−9=yMais um parecido para tentar
Exemplo 2Solving a System of Equations in Two Variables by GraphingSolve the following system of equations by graphing. Identify the type of system. 2x+y=−8 x−y=−1Mais um parecido para tentar
Exemplo 3Solving a System of Equations in Two Variables by SubstitutionSolve the following system of equations by substitution. −x+y=−5 2x−5y=1Mais um parecido para tentar
Exemplo 4Solving a System by the Addition MethodSolve the given system of equations by addition. x+2y=−1 −x+y=3
Exemplo 5Using the Addition Method When Multiplication of One Equation Is RequiredSolve the given system of equations by the addition method. 3x+5y=−11 x−2y=11Mais um parecido para tentar
Exemplo 6Using the Addition Method When Multiplication of Both Equations Is RequiredSolve the given system of equations in two variables by addition. 2x+3y=−16 5x−10y=30
Exemplo 7Using the Addition Method in Systems of Equations Containing FractionsSolve the given system of equations in two variables by addition. x/3 +y/6 =3 x/2 −y/4 =1Mais um parecido para tentar
Exemplo 8Solving an Inconsistent System of EquationsSolve the following system of equations. x=9−2y x+2y=13Mais um parecido para tentar
Exemplo 9Finding a Solution to a Dependent System of Linear EquationsFind a solution to the system of equations using the addition method. x+3y=2 3x+9y=6Mais um parecido para tentar
Exemplo 10Finding the Break-Even Point and the Profit Function Using SubstitutionGiven the cost function C(x)=0.85x+35,000 and the revenue function R(x)=1.55x, find the break-even point and the profit function.
Exemplo 11Writing and Solving a System of Equations in Two VariablesThe cost of a ticket to the circus is $25.00 for children and $50.00 for adults. On a certain day, attendance at the circus is 2,000 and the total gate revenue is $70,000. How many children and how many adults bought…Mais um parecido para tentar

Algebra and Trigonometry11.2 Systems of Linear Equations: Three Variables

Exemplo 1Determining Whether an Ordered Triple Is a Solution to a SystemDetermine whether the ordered triple ( 3,−2,1) is a solution to the system. x+y+z=2 6x−4y+5z=31 5x+2y+2z=13
Exemplo 2Solving a System of Three Equations in Three Variables by EliminationFind a solution to the following system: x−2y+3z=9 (1) −x+3y−z=−6 (2) 2x−5y+5z=17 (3)
Exemplo 3Solving a Real-World Problem Using a System of Three Equations in Three VariablesIn the problem posed at the beginning of the section, John invested his inheritance of $12,000 in three different funds: part in a money-market fund paying 3% interest annually; part in municipal bonds paying 4%…Mais um parecido para tentar
Exemplo 4Solving an Inconsistent System of Three Equations in Three VariablesSolve the following system. x−3y+z=4 (1) −x+2y−5z=3 (2) 5x−13y+13z=8 (3)Mais um parecido para tentar
Exemplo 5Finding the Solution to a Dependent System of EquationsFind the solution to the given system of three equations in three variables. 2x+y−3z=0 (1) 4x+2y−6z=0 (2) x−y+z=0 (3)Mais um parecido para tentar

Algebra and Trigonometry11.3 Systems of Nonlinear Equations and Inequalities: Two Variables

Exemplo 1Solving a System of Nonlinear Equations Representing a Parabola and a LineSolve the system of equations. x−y=−1 y=x^2 +1Mais um parecido para tentar
Exemplo 2Finding the Intersection of a Circle and a Line by SubstitutionFind the intersection of the given circle and the given line by substitution. x^2 +y^2 =5 y=3x−5Mais um parecido para tentar
Exemplo 3Solving a System of Nonlinear Equations Representing a Circle and an EllipseSolve the system of nonlinear equations. x^2 +y^2 =26 (1) 3x^2 +25y^2 =100 (2)Mais um parecido para tentar
Exemplo 4Graphing an Inequality for a ParabolaGraph the inequality y>x^2 +1.
Exemplo 5Graphing a System of InequalitiesGraph the given system of inequalities. x^2 −y≤0 2x^2 +y≤12Mais um parecido para tentar

Algebra and Trigonometry11.4 Partial Fractions

Exemplo 1Decomposing a Rational Function with Distinct Linear FactorsDecompose the given rational expression with distinct linear factors. (3x)/(( x+2)( x−1))Mais um parecido para tentar
Exemplo 2Decomposing with Repeated Linear FactorsDecompose the given rational expression with repeated linear factors. (−x^2 +2x+4)/(x^3 −4x^2 +4x)Mais um parecido para tentar
Exemplo 3Decomposing P( x ) Q( x ) When Q(x) Contains a Nonrepeated Irreducible Quadratic FactorFind a partial fraction decomposition of the given expression. (8x^2 +12x−20)/(( x+3)( x^2 +x+2))Mais um parecido para tentar
Exemplo 4Decomposing a Rational Function with a Repeated Irreducible Quadratic Factor in the DenominatorDecompose the given expression that has a repeated irreducible factor in the denominator. (x^4 +x^3 +x^2 −x+1)/(x ( x^2 +1) ^2)Mais um parecido para tentar

Algebra and Trigonometry11.5 Matrices and Matrix Operations

Exemplo 1Finding the Dimensions of the Given Matrix and Locating EntriesGiven matrix A: ⓐWhat are the dimensions of matrix A? ⓑWhat are the entries at a31 and a22? A=[ 2 1 0 2 4 7 3 1 −2 ]
Exemplo 2Finding the Sum of MatricesFind the sum of A and B, given A=[ a b c d ] and B=[ e f g h ]
Exemplo 3Adding Matrix A and Matrix BFind the sum of A and B. A=[ 4 1 3 2 ] and B=[ 5 9 0 7 ]
Exemplo 4Finding the Difference of Two MatricesFind the difference of A and B. A=[ −2 3 0 1 ] and B=[ 8 1 5 4 ]
Exemplo 5Finding the Sum and Difference of Two 3 x 3 MatricesGiven A and B: ⓐFind the sum. ⓑFind the difference. A=[ 2 −10 −2 14 12 10 4 −2 2 ]and B=[ 6 10 −2 0 −12 −4 −5 2 −2 ]Mais um parecido para tentar
Exemplo 6Multiplying the Matrix by a ScalarMultiply matrix A by the scalar 3. A=[ 8 1 5 4 ]Mais um parecido para tentar
Exemplo 7Finding the Sum of Scalar MultiplesFind the sum 3A+2B. A=[ 1 −2 0 0 −1 2 4 3 −6 ]and B=[ −1 2 1 0 −3 2 0 1 −4 ]
Exemplo 8Multiplying Two MatricesMultiply matrix A and matrix B. A=[ 1 2 3 4 ] and B=[ 5 6 7 8 ]
Exemplo 9Multiplying Two MatricesGiven A and B: ⓐ Find AB. ⓑ Find BA. A=[ −1 2 3 4 0 5 ]and B=[ 5 −4 2 −1 0 3 ]
Exemplo 11Using a Calculator to Perform Matrix OperationsFind AB−C given A=[ −15 25 32 41 −7 −28 10 34 −2 ],B=[ 45 21 −37 −24 52 19 6 −48 −31 ],and C=[ −100 −89 −98 25 −56 74 −67 42 −75 ].

Algebra and Trigonometry11.6 Solving Systems with Gaussian Elimination

Exemplo 1Writing the Augmented Matrix for a System of EquationsWrite the augmented matrix for the given system of equations. x+2y−z=3 2x−y+2z=6 x−3y+3z=4Mais um parecido para tentar
Exemplo 2Writing a System of Equations from an Augmented Matrix FormFind the system of equations from the augmented matrix. [ 1 −3 −5 2 −5 −4 −3 5 4 | −2 5 6 ]Mais um parecido para tentar
Exemplo 3Solving a 2×2 System by Gaussian EliminationSolve the given system by Gaussian elimination. 2x+3y=6 x−y=1/2Mais um parecido para tentar
Exemplo 4Using Gaussian Elimination to Solve a System of EquationsUse Gaussian elimination to solve the given 2×2 system of equations. 2x+y=1 4x+2y=6
Exemplo 5Solving a Dependent SystemSolve the system of equations. 3x+4y=12 6x+8y=24
Exemplo 6Performing Row Operations on a 3×3 Augmented Matrix to Obtain Row-Echelon FormPerform row operations on the given matrix to obtain row-echelon form. [ 1 −3 4 2 −5 6 −3 3 4 | 3 6 6 ]Mais um parecido para tentar
Exemplo 7Solving a System of Linear Equations Using MatricesSolve the system of linear equations using matrices. x−y+z=8 2x+3y−z=−2 3x−2y−9z=9
Exemplo 8Solving a Dependent System of Linear Equations Using MatricesSolve the following system of linear equations using matrices. −x−2y+z=−1 2x+3y=2 y−2z=0Mais um parecido para tentar
Exemplo 9Solving Systems of Equations with Matrices Using a CalculatorSolve the system of equations. 5x+3y+9z=−1 −2x+3y−z=−2 −x−4y+5z=1
Exemplo 10Applying 2 × 2 Matrices to FinanceCarolyn invests a total of $12,000 in two municipal bonds, one paying 10.5% interest and the other paying 12% interest. The annual interest earned on the two investments last year was $1,335. How much was invested at…
Exemplo 11Applying 3 × 3 Matrices to FinanceAva invests a total of $10,000 in three accounts, one paying 5% interest, another paying 8% interest, and the third paying 9% interest. The annual interest earned on the three investments last year was $770. The…Mais um parecido para tentar

Algebra and Trigonometry11.7 Solving Systems with Inverses

Exemplo 1Showing That the Identity Matrix Acts as a 1Given matrix A, show that AI=IA=A. A=[ 3 4 −2 5 ]
Exemplo 2Showing That Matrix A Is the Multiplicative Inverse of Matrix BShow that the given matrices are multiplicative inverses of each other. A=[ 1 5 −2 −9 ],B=[ −9 −5 2 1 ]Mais um parecido para tentar
Exemplo 3Finding the Multiplicative Inverse Using Matrix MultiplicationUse matrix multiplication to find the inverse of the given matrix. A=[ 1 −2 2 −3 ]
Exemplo 4Using the Formula to Find the Multiplicative Inverse of Matrix AUse the formula to find the multiplicative inverse of A=[ 1 −2 2 −3 ]Mais um parecido para tentar
Exemplo 5Finding the Inverse of the Matrix, If It ExistsFind the inverse, if it exists, of the given matrix. A=[ 3 6 1 2 ]
Exemplo 6Finding the Inverse of a 3 × 3 MatrixGiven the 3×3 matrix A, find the inverse. A=[ 2 3 1 3 3 1 2 4 1 ]Mais um parecido para tentar
Exemplo 7Solving a 2 × 2 System Using the Inverse of a MatrixSolve the given system of equations using the inverse of a matrix. 3x+8y=5 4x+11y=7
Exemplo 8Solving a 3 × 3 System Using the Inverse of a MatrixSolve the following system using the inverse of a matrix. 5x+15y+56z=35 −4x−11y−41z=−26 −x−3y−11z=−7Mais um parecido para tentar
Exemplo 9Using a Calculator to Solve a System of Equations with Matrix InversesSolve the system of equations with matrix inverses using a calculator 2x+3y+z=32 3x+3y+z=−27 2x+4y+z=−2

Algebra and Trigonometry11.8 Solving Systems with Cramer's Rule

Exemplo 1Finding the Determinant of a 2 × 2 MatrixFind the determinant of the given matrix. A=[ 5 2 −6 3 ]
Exemplo 2Using Cramer’s Rule to Solve a 2 × 2 SystemSolve the following 2×2 system using Cramer’s Rule. 12x+3y=15 2x−3y=13Mais um parecido para tentar
Exemplo 3Finding the Determinant of a 3 × 3 MatrixFind the determinant of the 3 × 3 matrix given A=[ 0 2 1 3 −1 1 4 0 1 ]Mais um parecido para tentar
Exemplo 4Solving a 3 × 3 System Using Cramer’s RuleFind the solution to the given 3 × 3 system using Cramer’s Rule. x+y−z=6 3x−2y+z=−5 x+3y−2z=14Mais um parecido para tentar
Exemplo 5Using Cramer’s Rule to Solve an Inconsistent SystemSolve the system of equations using Cramer’s Rule. 3x−2y=4 (1) 6x−4y=0 (2)
Exemplo 6Use Cramer’s Rule to Solve a Dependent SystemSolve the system with an infinite number of solutions. x−2y+3z=0 (1) 3x+y−2z=0 (2) 2x−4y+6z=0 (3)
Exemplo 7Illustrating Properties of DeterminantsIllustrate each of the properties of determinants.
Exemplo 8Using Cramer’s Rule and Determinant Properties to Solve a SystemFind the solution to the given 3 × 3 system. 2x+4y+4z=2 (1) 3x+7y+7z=−5 (2) x+2y+2z=4 (3)