Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Practice and Problem-Solving Exercises - Page 371: 20


$x=5$ $y=2$

Work Step by Step

#$1$ The first step to solving systems of equations by substitution is to get one equation equal to one variable. This is more easily done in the first equation by subtracting 3 and 3y from both sides of the equation. Then simplify the second equation for easier substitution later by dividing by the greatest common multiple on both sides of the equation. $y=x-3$ $x+2y=9$ #$2$ The next step is to substitute y for its equivalent and then solve for the only remaining variable, x. $x+2(x-3)=9$ $x + 2x-6=9$ $3x-6=9$ .......+6 .....+6 $3x=15$ $3x\div3=15\div3$ $x=5$ #$3$ Substitute value of x into 1st or 2nd equation. We use first equation to solve for y. $y= 5 - 3$ $y=2$ #$4$ The answer is $x=5$ , $y=2$
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