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