Question

How do you solve -3x - 2y = -13 and -5x -y = -17

Answer 1

`\left\{\begin{array}{ccc}-3x-2y=-13\\-5x-y=-17&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-3x-2y=-13\\10x+2y=34\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad7x=21\qquad\text{divide both sides by 7}\\.\qquad\boxed{x=3}\\\\\text{Put the value of x to the second equation}\\\\-5(3)-y=-17\\\\-15-y=-17\qquad\text{add 15 to both sides}\\\\-y=-2\qquad\text{change the signs}\\\\\boxed{y=2}\\\\Answer:\ \boxed{x=3\ and\ y=2\to(3,\ 2)}`