## Algebra 2 Common Core

Published by Prentice Hall

# Chapter 3 - Linear Systems - 3-2 Solving Systems Algebraically - Practice and Problem-Solving Exercises: 29

#### Answer

$x = 1$, $y=1$, or $(1,1)$

#### Work Step by Step

Given: $5x - y = 4$ $2x - y = 1$ Remember that '$-(-y) = +y$. Subtract the second equation, $2x - y = 1$, from the first, $5x - y = 4$: $5x - y - (2x - y) = 4 -(1) \\5x-y-2x+y=3$ Combine like terms: $3x = 3$ Divide both sides by $3$: $x = 1$ Substitute $x = 1$ into the second equation: $2x-y=1 \\2(1) - y = 1 \\2-y=1$ Expand the brackets: $2 - y = 1$ Subtract $2$ from both sides: $-y = 1-2 \\-y-=1$ Divide both sides by $-1$: $y = 1$ Thus, $x = 1$, $y=1$

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