Question

How do you solve the following system: #5x+2y=20 , 3x+4y=-10 #?

Answer 1

The solution for the system of equations is:

`color(blue)(x=50/7`

`color(blue)(y = -55/7`

Explanation:

`5x+2y=20`, multiplying by `2`
`10x+color(blue)(4y)=40`.......equation `(1)`

`3x +color(blue)(4y)=-10`.....equation `(2)`

Solving by elimination.

Subtracting equation `(2)` from `(1)` results in elimination of `color(blue)(4y`

`10x+cancelcolor(blue)(4y)=40`
`-3x -cancelcolor(blue)(4y)=10`

`7x=50`

`color(blue)(x=50/7`

Finding `y` from equation `1`

`5x+2y=20`

`2y=20 -5x`

`2y=20 -5 xx 50/7`

`2y=20 - 250/7`

`2y=140/7 - 250/7`

`2y=- 110/7`

`y=- 110/(7 xx2)`

`color(blue)(y = -55/7`