Question

What are x and y if `5x - 2y = -5` and `y - 5x = 3`?

Answer 1

`color(brown)(x = -1/5, y = 2`

Explanation:

`5 x - 2 y = -5, " Eqn (1)"`

`y - 5 x = 3, " Eqn (2)"`

`y = 5x + 3`

Substituting value of y in terms of x in Eqn (1)"#,

`5x - 2*(5x + 3) = -5`

`5x - 10x - 6 = -5`

`-5x = -1, x = -1/5`

`y = 5x + 3 = 5 * (-1/5) + 3 = 2`

Answer 2

The solution is `(-1/5,2)` or `(-0.2,2)`.

Explanation:

We can also use elimination to solve this system of linear equations.

`"Equation 1":` `5x-2y=-5`

`"Equation 2":` `y-5x=3`

Rewrite Equation 2:

`-5x+y=3`

Add: Equation 1 + Equation 2:

`-5x + color(white)(.)y =color(white)(....)3`
`ul(color(white)(..)5x-2y=-5)`
`color(white)(........)-y=-2`

Divide both sides by `-1`. This will reverse the signs.

`y=2`

Substitute `2` for `y` in Equation 2 (either equation will work).

`2-5x=3`

Subtract `2` from both sides.

`-5x=3-2`

`-5x=1`

Divide both sides by `-5`.

`x=-1/5`

The solution is `(-1/5,2)` or `(-0.2,2)`.

graph{(5x-2y+5)(y-5x-3)=0 [-10, 10, -5, 5]}