Question

Solve this system of equation by substitution
-2x-y=-9
5x-2y=18

Answer 1

-2x - y = -9
y = -2x + 9

5x-2(-2x + 9) = 18
5x - (-4x +18) = 18
9x -18 = 18
9x = 36
x=4

-2x - y = -9
-2(4) - y = -9
-8 - y = -9
-y = -1
y = 1
Point of intersection: (4,1)

Answer 2

`\begin{cases} -2x-y=-9 \\ 5x-2y=18 \end{cases}\\\\ \begin{cases} y=-2x+9 \\ 5x-2y=18 \end{cases}\\\\substitution \\\\ 5x-2 \cdot (-2x+9)=18 \\5x+4x-18=18 \\9x-18+18\\9x=36\ \ /:9\\x=(36)/(9)\\x=4\\=================\\y=-2x+9 \\y=-2 \cdot 4+9 =-8+9=1\\ \\Answer:\\\\\begin{cases} x=4 \\ y=1 \end{cases}`