Question

How do you solve the following system?: `3x +2y = 7 , -2x - 2y = -4`

Answer 1

The solution for the system of equations is:

`color(green)(x=3`
`color(green)(y=-1`

Explanation:

`3x+color(blue)(2y)=7`.................equation `(1)`
`-2x -color(blue)(2y) =-4`.......equation `(2)`

Solving by elimination

Adding equations `(1)` and `(2)` eliminates `color(blue)(2y)`

`3x+cancelcolor(blue)(2y)=7`
`-2x -cancelcolor(blue)(2y) =-4`

`color(green)(x=3`

Finding `y` by substituting the value of `x` in equation `1:`

`3x+2y=7`

`2y=7-3x`

`2y=7-3 * color(green)(3`

`2y=7-9`

`2y=-2`

`y=-2/2`

`color(green)(y=-1`