Question

How do i solve 3x+y=13, 5x-2y=18 using the substitution method

Answer 1

$\left\{\begin{array}{ccc}3x-y=13&\text{multiply both sides by (-2)}\\5x-2y=18\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-6x+2y=-26\\5x-2y=18\end{array}\right}\\.\qquad-x=-8\qquad\text{change the signs}\\.\qquad\boxed{x=8}\\\\\text{Put the value of x to the first equation}\\\\3(8)-y=13\\\\24-y=13\qquad\text{subtract 24 from both sides}\\\\-y=-11\qquad\text{change the signs}\\\\\boxed{y=11}\\\\Answer:\ \boxed{x=8\ and\ y=11\to(8,\ 11)}$