Question D.3: Solve for x and y: -x + 2y = 3, 3x - 2y=-2
Solve for x and y:
\begin{aligned}-x+2 y &=3 \\3 x-2 y &=-2 \\\hline\end{aligned}.
In this example, note the effect of the minus sign and the use of parentheses to ensure that the proper sign is obtained for each product:
x=\frac{\left|\begin{array}{rr}3 & 2 \\-2 & -2\end{array}\right|}{\left|\begin{array}{rr}-1 & 2 \\3 & -2\end{array}\right|}=\frac{(3)(-2)-(-2)(2)}{(-1)(-2)-(3)(2)}=\frac{-6+4}{2-6}=\frac{-2}{-4}=\frac{1}{2}.
y=\frac{\left|\begin{array}{rr}-1 & 3 \\3 & -2\end{array}\right|}{-4}=\frac{(-1)(-2)-(3)(3)}{-4}.
=\frac{2-9}{-4}=\frac{-7}{-4}=\frac{7}{4}.
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