## Algebra 1

Published by Prentice Hall

# Chapter 2 - Solving Equations - 2-1 Solving One-Step Equations - Lesson Check: 9

#### Answer

x = 11$\frac{1}{3}$ y = 10$\frac{2}{3}$

#### Work Step by Step

$\frac{1}{3}y$ - $\frac{2}{3}x$ = -4 (Equation 1) 5x - 4y = 14 (Equation 2) Multiply equation (1) by 3 y - 2x = -12 (Equation 3) 5x - 4y = 14 Multiply equation (1) by 4 4y - 8x = -48 5x - 4y = 14 Rearrange to make y the subject 4y = 8x - 48 4y= 5x - 14 Therefore: 8x - 48 = 5x - 14 3x = 34 x = 11$\frac{1}{3}$ Substitute x in a previous equation to find y: y - 2x = -4 (Rearranged to =>) y = -12 + 2x y = -12 + 2(11$\frac{1}{3}$) y = 10$\frac{2}{3}$ Proof: $\frac{1}{3}$(10$\frac{2}{3}$) - $\frac{2}{3}$(11$\frac{1}{3}$) = -4 5(11$\frac{1}{3}$)-4(10$\frac{2}{3}$) = 14

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