Question

How do you solve y= 3/4x+3 and 2x-4y=6?

Answer 1

`(x, y) = (-18, -21/2)`

Explanation:

Given
[1]`color(white)("XXX")y=3/4x+3`
[2]`color(white)("XXX")2x-4y=6`

Using [1], substitute `3/4x+3` for `y` in [2]
[3]`color(white)("XXX")2x-4(3/4x+3) = 6`

[4]`color(white)("XXX")2x-3x-12 = 6`

[5]`color(white)("XXX")-x = 18`

[6]#color(white)("XXX")x = -18

Substitute `(-18)` for `x` in[2]
[7]`color(white)("XXX")2(-18)-4y=6`

[8]`color(white)("XXX")-4y = 42`

[9]`color(white)("XXX")y = -21/2`

Answer 2

`x=-18`
`y=-21/2`

Explanation:

`y=3/4x+3`---------------(1)
`2x-4y=6`-----------------(2)

Substitute the value of y from equation (1) in equation (2)

`2x -4(3/4x+3)=6`
`2x-3x-12=6`
`-x=6+12=18`
`x=-18`

Substitute x value in equation (2)

`2(-18) -4y = 6`
`-36-4y = 6`
`-4y = 6 + 36 = 42`
`y = 42/-4 = -21/2`