Question

What is the solution of the system of equations `2x-5y=11` and `-2x+3y=-9`?

Answer 1

`x = 3, y = -1`

Explanation:

If we are working with simultaneous equations in this form, the best combination of one of the variables is to have them as additive inverses, because their sum is 0.

This is exactly what we have in the equations below.
Adding the equations will eliminate the x terms.

`color(white)(xxxxxxxx)color(red)(2x)-5y = 11 " "A`
`color(white)(xxxxxx.)color(red)(-2x) +3y =-9 " "B`

`A+Bcolor(white)(xxxxxx)-2y =2" "larr div -2`

`color(white)(xxxxxxxxxxxxx)y =-1" "larr` we know y, now find x.

Subs in A: `" "2x -5y = 11`

`color(white)(xxxxxx)2x -5(-1) =11`

`color(white)(xxxxxxxxxx)2x+5 = 11`

`color(white)(xxxxx.xxxxxxxx)2x = 6`

`color(white)(xxxxxxxxxxxxxx)x=3`