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Exercises Systems of equations

Example 9 from Algebra and Trigonometry, 11.1 Systems of Linear Equations: Two Variables

Finding a Solution to a Dependent System of Linear Equations

Find a solution to the system of equations using the addition method.

\begin{matrix} x + 3 y = 2 \\ 3 x + 9 y = 6 \end{matrix}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
With the addition method, we want to eliminate one of the variables by adding the equations. In this case, let’s focus on eliminating $x .$ If we multiply both sides of the first equation by $−3,$ then we will be able to eliminate the $x$ -variable.
$\begin{array}{l} x + 3 y = 2 \\ (−3) (x + 3 y) = (−3) (2) \\ −3 x - 9 y = - 6 \end{array}$
Now add the equations.

$\begin{array}{l} \underset{______________}{\begin{array}{l} - 3 x - 9 y & = −6 \\ + 3 x + 9 y & = 6 \end{array}} \\ \begin{array}{l} 0 & = 0 \end{array} \end{array}$
We can see that there will be an infinite number of solutions that satisfy both equations.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the following system of equations in two variables.

\begin{array}{l} \begin{array}{l} y−2x=5 \end{array} \\ −3 y + 6 x = −15 \end{array}

How did it go?

PreviousSolving an Inconsistent System of Equations Next Finding the Break-Even Point and the Profit Function Using Substitution

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 11.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.