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: 5


The solution is $(-3, 5)$.

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 $y$ term: $x + 2y = 7$ $-x + 3y = 18$ _____________ $2y = 7$ $3y = 18$ Now we add both sides of the two equations to get: $5y = 25$ Divide each side by $5$ to solve for $y$: $y = 5$ 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: $x + 2(5) = 7$ Multiply: $x + 10 = 7$ Subtract $10$ from each side of the equation to isolate the variable on one side and constants on the other: $x = -3$ The solution is $(-3, 5)$.
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