Question

Solve the following system of equations -7x+2y=9, -8x+9y=17

Answer 1

`\left\{\begin{array}{ccc}-7x+2y=9&|\cdot9\\-8x+9y=17&|\cdot(-2)\end{array}\right\\ \left\{\begin{array}{ccc}-63x+18y=81\\16x-18y=-34\end{array}\right\ |\text{add both sides of equations}\\-47x=47\ \ \ |:(-47)\\.\ \ \ \ x=-1\\\\\text{substitute the value of x to the first equation}\\\\-7(-1)+2y=9\\7+2y=9\ \ \ |-7\\2y=2\ \ \ |:2\\y=1\\\\\text{Answer:}\ x=-1\ and\ y=1\to(-1;\ 1)`

Answer 2

-7x+2y=9 | * 9
-8x+9y=17 | *(-2)


-63x + 18y = 81
16x -18y = -34

_______________ +

-47x = 47 ⇒ x = -1


7+2y=9 ⇒ 2y = 9-7 ⇒ y = 1