Question

How do you solve the system of linear equations `y= - 2+ 3x` and `y = - 14+ 6x` by substitution?

Answer 1

`(x,y)=(4,10)`
`color(white)("XXX")`see below for method using substitution

Explanation:

Given
[1]`color(white)("XXX")y=-2+3x`
[2]`color(white)("XXX")y=-14+6x`

From [2] we know we can substitute `-14+6x` for `y` in [1]
[3]`color(white)("XXX")-14+6x=-2+3x`

Adding `14` to both sides:
[4]`color(white)("XXX")6x=12+3x`

then subtracting `3x` from both sides
[5]`color(white)("XXX")3x=12`

and dividing both sides by `3`
[6]`color(white)("XXX")x=4`

From [5] we now know that we can substitute `4` for `x` in [1]
[6]`color(white)("XXX")y=-2+3xx4`

After simplifying
[7]`color(white)("XXX")y=10`

So `(x,y)=(4,10)`