## Algebra 1

Published by Prentice Hall

# Chapter 6 - Systems of Equations and Inequalities - Put it All Together - Page 403: Task 2

#### Answer

$x =2$, $y =6$

#### Work Step by Step

$x + 2y = 14$ $3x + 5/4*y +5/4y = 21$ $x + 2y = 14$ $3x + 10/4*y = 21$ (combining like terms) $x + 2y = 14$ $x + 2y-2y = 14-2y$ $x = 14-2y$ (isolating one variable) $x = 14-2y$ $3x + 10/4*y = 21$ $3x + 10/4*y = 21$ $3*(14-2y) + 10/4*y = 21$ (substituting one variable for another) $42 -6y +10/4*y = 21$ $42 -14/4*y = 21$ (combining like terms) $42-14/4*y -42 = 21-42$ (eliminating the constant from one side of the equation) $-14/4*y = -21$ (combining like terms) $-14/4*y *-4/14 = -21*-4/14$ (eliminating the constant by the variable) $y = 84/14 = 6$ $y=6$ (simplifying the constants) $x +2y = 14$ $x + 2*6 = 14$ (substituting 6 for y) $x +12 = 14$ (simplifying the equation) $x + 12 - 12 = 14 - 12$ (eliminating the constant) $x = 2$ (combining like terms)

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