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

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