Question

How do you solve `y= -8x-3 and y=4x-3?`

Answer 1

`x=0 and y=-3`

Explanation:

You might notice that both equations represent straight lines as they are both in the form `y=mx+c`.

By solving them you are finding the point of intersection of the two lines.

The easiest way to solve equation in this form is to equate the equations. They are both given as `y=...`

`color(blue)(y = -8x-3)" " and " "color(red)(y = 4x-3)`

`color(white)(xxxxxxxxxxxx)color(blue)(y) = color(red)(y )`

`color(white)(xxxxx):. color(blue)(-8x-3) = color(red)(4x-3)`

`color(white)(xxxxx):. -3+3 = 4x+8x`
`color(white)(xxxxxxxxxx):. 0= 12x`
`color(white)(xxxxxxxxxx):. 0= x`

(We could have seen this at the beginning because the `3` is subtracted from different terms in `x`, yet both give `y`.
`x =0` is the only possible value of `x`

`y = 4(0)-3 =-3`