Introductory Algebra for College Students (7th Edition)

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

Chapter 4 - Section 4.3 - Solving Systems of Linear Equations by the Addition Method - Exercise Set - Page 310: 6


The solution is $(-3, 4)$.

Work Step by Step

The coefficients of the $x$ term differ only in sign, so if we add these equations without modification, we will cancel out the $x$ term and can then solve for $y$: Let us add the equations. First, we cancel out the $x$ term: $2x + y = -2$ $-2x - 3y = -6$ _____________ $y = -2$ $-3y = -6$ Now we add both sides of the two equations to get: $-2y = -8$ Divide each side by $-2$ to solve for $y$: $y = 4$ Now that we have the value for $y$, we can plug this value into one of the equations to solve for $x$. Let's use the first equation: $2x + 4 = -2$ Subtract $4$ from each side of the equation to isolate the variable on one side of the equation and constants on the other: $2x = -6$ Divide each side of the equation by $2$ to solve for $x$: $x = -3$ The solution is $(-3, 4)$.
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