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: 8


The solution is $(\frac{17}{7}, 1)$.

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: $7x - 4y = 13$ $-7x + 6y = -11$ _____________ $-4y = 13$ $6y = -11$ Now we add both sides of the two equations to get: $2y = 2$ Divide both sides of the equation by $2$ to solve for $y$: $y = 1$ 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: $7x - 4(1) = 13$ Multiply: $7x - 4 = 13$ Add $4$ to each side of the equation to isolate the variable on one side of the equation and constants on the other: $7x = 17$ Divide each side of the equation by $7$ to solve for $x$: $x = \frac{17}{7}$ The solution is $(\frac{17}{7}, 1)$.
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