Question

How do you solve the system of equations `-8x + 9y = - 37` and `- 15x + 2y = 5`?

Answer 1

`x =-1 and y=-5`

Explanation:

The equations can be solved by the elimination method. Let's make the coefficients of `y` the same, but make one positive and the other negative.

`color(white)(wwwwwww.w)-8x+9y =-37" ".............A`
`color(white)(wwwwwwww)-15x+2y =+5" "...............B`

`Axx2rarr" " -16xcolor(blue)(+18y) = -74" "...........C`
`Bxx -9 rarr" "135xcolor(blue)(-18y)= -45" "............D`

`C+Drarr" "119xcolor(white)(wwww) =-119`

`color(white)(wwwwwwwwwww..www)x=-1`

Now that you know the value of `x`, substitute to find `y`

`color(white)(wwwwwww)-8(-1)+9y =-37" ".............A`
`color(white)(wwwwwwwww.ww.w)+9y =-37-8`
`color(white)(wwwwwwwwwww.ww.w)9y =-45`
`color(white)(wwwwwwwww.wwwww.w)y =-5`