Question

Multiply each equation by a constant that would help to eliminate the y terms. 2x-5y=-21 3x-3y=-18

Answer 1

$\left\{\begin{array}{ccc}2x-5y=-21&\text{multiply both sides by 3}\\3x-3y=-18&\text{multiply both sides by (-5)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}6x-15y=-63\\-15x+15y=90\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-9x=27$

$\text{solution:}\\\\-9x=27\qquad\text{divide both sides by 9}\\x=-3\\\\\text{Substitute the value of x to the first equation:}\\\\2(-3)-5y=-21\\-6-5y=-21\qquad\text{add 6 to both sides}\\-5y=-15\qquad\text{divide both sides by (-5)}\\y=3\\\\\boxed{x=-3\ and\ y=3}$