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: 4

Answer

The solution is $(4, 1)$.

Work Step by Step

The coefficients of the $y$ term differ only in sign, so if we add these equations without modification, we will cancel out the $y$ term and can then solve for $x$: Let us add the equations. First, we cancel out the $y$ term: $3x + 2y = 14$ $3x - 2y = 10$ _____________ $3x = 14$ $3x = 10$ Now we add both sides of the two equations to get: $6x = 24$ Divide each side by $6$ to solve for $x$: $x = 4$ Now that we have the value for $x$, we can plug this value into one of the equations to solve for $y$. Let's use the first equation: $3(4) + 2y = 14$ Multiply: $12 + 2y = 14$ Subtract $12$ from each side of the equation to isolate the variable on one side and constants on the other: $2y = 2$ Divide both sides by $2$ to solve for $y$: $y = 1$ The solution is $(4, 1)$.
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