Question

How do you solve the system of equations `5x + y = 24` and `- 3x + 2y = - 4`?

Answer 1

`x=4` and `y=4`

Explanation:

`5x+y=24`
`-3x+2y=-4`

Multiply all terms in the first equation by `2`.

`10x+2y=48`
`-3x+2y=-4`

Subtract the second equation from the first equation.

`10x+2y=48`
`-(-3x+2y)=-(-4)`

Opening the brackets in the second equation we get:

`10x+2y=48`
`+3x-2y=+4`

Simplifying we get:

`13x=52`

Divide both sides by `13`.

`x=4`

Substitute `4` for `x` in either of the given equations.

1. `5x+y=24`
   `(5xx4)+y=24`
   `20+y=24`
   Subtract 20 from each side.
   `y=4`

2. `-3x+2y=-4`
   `(-3xx4)+2y=-4`
   `-12+2y=-4`
   Add `12` to both sides.
   `2y=8`
   Divide both sides by `2`.
   `y=4`

`:.y=4`