## Intermediate Algebra: Connecting Concepts through Application

$x = 3.2$ $y = 4.2$ OR $(3.2, 4.2)$
$5x + 12y = 66.4$ $5x = 66.4 - 12y$ $x = \frac{66.4-12y}{5}$ $-4x + 10y = 29.2$ $-4(\frac{66.4-12y}{5}) + 10y = 29.2$ $-4(66.4-12y) + 5(10y) = 5(29.2)$ $-265.6+48y + 50y =146$ $98y - 411.6 = 0$ $98y = 411.6$ $y = 4.2$ $x = \frac{66.4-12(4.2)}{5}$ $= \frac{66.4- 50.4}{5}$ $= \frac{16}{5}$ $x = 3.2$ Check: $5(3.2) + 12(4.2) \overset{?}{=}66.4$ $16 + 50.4 \overset{?}{=} 66.4$ $66.4 = 66.4$ $-4(3.2) + 10(4.2) \overset{?}{=} 29.2$ $-12.8 + 42 \overset{?}{=} 29.2$ $29.2 = 29.2$