Question

How do you solve the system of equations `4x = 2y + 10` and `2x - 2y = 7`?

Answer 1

`x=3/2 and y =-2`

Explanation:

The `y` terms already have their coefficients the same with opposite signs. This means that if the two equations are added, the `y` terms will be eliminated. `(+2y) +(-2y)=0`

Re-arrange the equations, then add them

`-4x+2y = -10` ..................................A
`ul(+2x-2y=+7)`......................................B
`-2x" "=-3`

`x = 3/2`

Now substitute into A to find `y`

`-4(3/2) +2y = -10`

`-6 +2y = -10`

`2y = -4`

`y =-2`

Check in B:

`2(3/2)-2(-2)`

`=3+4`

`=7`