How do you solve by substitution `5x-6y=6` and `5x+y=2`?

`5x-6y=6` --- (1)
`5x+y=2` --- (2)

(1) minus (2)

`-6y-y=6-2`
`-7y=4`
`y=-4/7` --- (3)

Sub (3) into (1)

`5x-6times-4/7=6`
`5x+24/7=6`
`5x=18/7`
`x=18/35`

Solve the system of equations.

`"Equation 1":` `5x-6y=6`

`"Equation 2":` `5x+y=2`

The solution to the system of linear equations is the point they have in common, the point of intersection. The system will be solved using substitution.

Solve Equation 2 for `y`.

`y=-5x+2`

Substitute `-5x+2` for `y` in Equation 1. Solve for `x`.

`5x-6(-5x+2)=6`

Expand.

`5x+30x-12=6`

Simplify.

`35x-12=6`

Add `12` to both sides.

`35x=6+12`

Simplify.

`35x=18`

Divide both sides by `35`.

`x=18/35` or `0.514`

Substitute `18/35` for `x` in Equation 2. Solve for `y`.

`5(18/35)+y=2`

Simplify `color(red)cancel(color(black)(5))^1(18/color(red)cancel(color(black)(35))^7)` to `18/7`.

`18/7+y=2`

Multiply both sides by `7`.

`color(red)cancel(color(black)(7))^1xx18/color(red)cancel(color(black)(7))^1+7xxy=2xx7`

Simplify.

`18+7y=14`

Subtract `18` from both sides.

`7y=14-18`

Simplify.

`7y=-4`

Divide both sides by `7`.

`y=-4/7` or `-0.571`

Solution

`(18/35,-4/7)` or `(0.514,-0.571)`

graph{(y-5/6x+1)(y+5x-2)=0 [-10, 10, -5, 5]}