Question

How do you solve the system of linear equations `x + 2y = 7` and `2x - 3y = -5`?

Answer 1

The solution for the system of equations is:
`color(blue)(x=11/7`

`color(blue)(y= 19/7`

Explanation:

`x+ 2y=7` , multiplying this equation by `2`
`color(blue)(2x)+ 4y=14`......equation `(1)`

`color(blue)(2x)- 3y=-5`.....equation `(2)`

Solving by elimination

Subtracting equation `2` from `1`

`cancelcolor(blue)(2x)+ 4y=14`

`-cancelcolor(blue)(2x) + 3y= 5`

`7y =19`

`color(blue)(y= 19/7`

Finding `x` from equation `1`:
`x+ 2y=7`

`x+ 2xx19/7=7`

`x+ 38/7=7`

`x=7 - 38/7`

`x=49/7 - 38/7`

`color(blue)(x=11/7`