Solve the following system of equations. 8x + 5y = -84 3x + y = -21 A. x = -12, y = -3 B. x = 5, y = -24.8 C. x = 12, y = -57 D. x = -3, y =

Solve the following system of equations.

8x + 5y = -84

3x + y = -21

A. x = -12, y = -3

B. x = 5, y = -24.8

C. x = 12, y = -57

D. x = -3, y = -12

The answer is D. x = -3 and y = -12

$$\small{
\begin{array}{lrcl}
(1) & 8x + 5y &=& -84 \\
\hline
(2) & 3x + y &=& -21 \qquad | \qquad \cdot 5\\
(2) & 15x + 5y &=& -105 \\
\hline
(2)-(1)& 15x-8x +5y-5y &=& -105 -(-84) \\
& 15x-8x &=& -105 + 84 \\
& 7x &=& -21 \qquad | \qquad :7\\
& \mathbf{x} & \mathbf{=} & \mathbf{-3} \\
\hline
&3x+y &=& -21\\
&3\cdot(-3) + y &=& -21\\
&-9 + y &=& -21\\
& y &=& -21 + 9 \\
& \mathbf{y} &\mathbf{=} & \mathbf{-12}
\end{array}
}$$