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Exercises Systems of equations

Example 5.19 from Elementary Algebra, 5.2 Solve Systems of Equations by Substitution

Solve Systems of Equations by Substitution: example 5.19

Solve the system by substitution. $\frac{3}{4} y + \frac{3}{2} .$

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
We need to solve one equation for one variable. We will solve the first equation for x.

Solve the first equation for x.

Substitute $\frac{3}{4} y + \frac{3}{2}$ for x in the second equation.

Replace the x with $\frac{3}{4} y + \frac{3}{2} .$

Solve for y.

Since 0 = 0 is a true statement, the system is consistent. The equations are dependent. The graphs of these two equations would give the same line. The system has infinitely many solutions.

Your turn

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

Solve the system by substitution. ${\begin{matrix} 2 x - 3 y = 12 \\ −12 y + 8 x = 48 \end{matrix}$

How did it go?

PreviousSolve Systems of Equations by Substitution: example 5.18 Next Solve Systems of Equations by Substitution: example 5.20

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 5.2, 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.