Chapter 6 - Systems of Equations and Inequalities - 6-3 Solving Systems Using Elimination - Practice and Problem-Solving Exercises - Page 378: 15

(3,1)

$2x+3y=9\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x+\ \ 3y=\ \ \ \ \ 9$ $\ \ x+5y=8\ \ \ \ $ multiply by-2$\ \ \ \ \ \ \ \ \ \ \underline{-2x-10y=-16}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -7y=\ -7$ Solve for y. $-7y=-7$ $-7y\div-7=-7\div-7$ $y=1$ Substitute 1 for y in either equation and solve for x. $x+5y=8$ $x+5(1)=8$ $x+5-5=8-5$ $x=3$