Question

How would I solve this system of equations? 2y+x=-17 5x-4y=-15

Answer 1

$\left\{\begin{array}{ccc}2y+x=-17\\5x-4y=-15\end{array}\right\\\\\left\{\begin{array}{ccc}x+2y=-17&\text{multiply both sides by 2}\\5x-4y=-15\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+4y=-34\\5x-4y=-15\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad7x=-49\qquad\text{divide both sides by 7}\\.\qquad\boxed{x=-7}\\\\\text{Put the value of x to the first equation:}\\\\2y+(-7)=-17\\2y-7=-17\qquad\text{add 7 to both sides}\\2y=-10\qquad\text{divide both sides by 2}\\\boxed{y=-5}\\\\Answer:\ \boxed{x=-7\ and\ y=-5\to(-7,\ -5)}$