Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 5 - Cumulative Review Exercises - Page 417: 15


The solution for this system of equations is $(3, -4)$.

Work Step by Step

We can use substitution to solve this system of equations because one of the equations already has $y$ isolated to one side. We use the second equation to substitute for $y$ in the first equation: $$2x + 3(3x - 13) = -6$$ Use distributive property first: $$2x + 9x - 39 = -6$$ Combine like terms: $$11x - 39 = -6$$ Add $39$ to each side of the equation to move all constants to the right side of the equation: $$11x = 33$$ Divide by $11$ on each side to solve for $x$: $$x = 3$$ Now that we have the value for $x$, we can plug it into the second equation to solve for $y$: $$y = 3(3) - 13$$ Multiply first, according to order of operations: $$y = 9 - 13$$ Subtract to solve for $y$: $$y = - 4$$ The solution for this system of equations is $(3, -4)$.
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