Question

Use the elimination method to solve the system

5x − 14y = 74
−x − 6y = 38

Answer 1

`\bf \begin{array}{llll} 5x-14y=74&\implies &~~5x-14y=74\\ -x-6y=38&\boxed{* 5}\implies &-5x-30y=190\\ &&--------\\ &&~~0x-44y=264 \end{array} \\\\\\ -44y=264\implies y=\cfrac{264}{-44}\implies \boxed{y=-6}\\\\ -------------------------------\\\\ 5x-14y=74\implies 5x-14(-6)=74\implies 5x+84=74 \\\\\\ 5x=-10\implies x=\cfrac{-10}{5}\implies \boxed{x=-2}`