## Intermediate Algebra: Connecting Concepts through Application

$(7, 15)$ or $x = 7$ $y = 15$
$y = 5x - 20$ $2x - 3y = -31$ $2x - 3(5x - 20) = -31$ $2x - 15x + 60 = -31$ $-13x + 60 + 31 = 0$ $-13x +91 = 0$ $-13x = -91$ $x = 7$ $y = 5(7) - 20$ $y = 35 - 20$ $y = 15$ Check: $2(7) - 3(15) \overset{?}{=} -31$ $14 - 45 \overset{?}{=} -31$ $-31 = -31$ $15 \overset{?}{=} 5(7) - 20$ $15 \overset{?}{=} 35 - 20$ $15 = 15$