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: 7


The solution is $(3, 1)$.

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: $5x - y = 14$ $-5x + 2y = -13$ _____________ $-y = 14$ $2y = -13$ Now we add both sides of the two equations to get: $y = 1$ 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: $5x - 1 = 14$ Add $1$ to each side of the equation to isolate the variable on one side of the equation and constants on the other: $5x = 15$ Divide each side of the equation by $5$ to solve for $x$: $x = 3$ The solution is $(3, 1)$.
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