Question

solve by elimination
x+2y=-7
x-5y=7

Answer 1

$\left \{ {{x+2y=-7} \atop {x-5y=7\ \ | multiply\ by\ -1}} \right. \\\\ \left \{ {{x+2y=-7} \atop {-x+5y=-7}} \right. \\+-----\\ addition\ method\\\\ 7y=-14 \ \ \ | divide\ by\ 7\\\\ y=-2\\\\ substitute\ y=-2\ to\ first\ equation\\\\x=-7-2y=-7+4=-3\\\\ x=-3$

Answer 2

$\left\{\begin{array}{ccc}x+2y=-7\\x-5y=7&|multiply\ both\ sides\ by\ (-1)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x+2y=-7\\-x+5y=-7\end{array}\right}\ \ \ \ |add\ both\ sides\ of the\ equations\\.\ \ \ \ \ \ \ \ 7y=-14\ \ \ \ |divide\ both\ sides\ by\ 7\\.\ \ \ \ \ \ \ \ \boxed{y=-2}\\\\put\ the\ value\ of\ "y"\ to\ the\ first\ equation:\\\\x+2\cdot(-2)=-7\\x-4=-7\ \ \ \ |add\ 4\ to\ the\ both\ sides\\\boxed{x=-3}\\\\Answer:\boxed{\boxed{\left\{\begin{array}{ccc}x=-3\\y=-2\end{array}}}$