Solve 12x + 7y = 81 and 5x - 4y = 13 by cross-multiplication. Find D, x and y.

Step 1. The numbers. $a_1 = 12$, $b_1 = 7$, $c_1 = -81$ and $a_2 = 5$, $b_2 = -4$, $c_2 = -13$.

Step 2. The three numbers. $X = b_1c_2 - b_2c_1 = 7(-13) - (-4)(-81) = -91 - 324 = -415$.

$Y = c_1a_2 - c_2a_1 = (-81)(5) - (-13)(12) = -405 + 156 = -249$.

$D = a_1b_2 - a_2b_1 = 12(-4) - 5(7) = -48 - 35 = -83$.

Step 3. Divide. $x = \dfrac{-415}{-83} = 5$ and $y = \dfrac{-249}{-83} = 3$.