Question

How do you solve the system `y = 4x - 3` and `y = - 3x - 3` by graphing?

Answer 1

`x = 0` and `y = -3`

Explanation:

Because the second equation has already be solved for `y` we can substitute `color(red)(-3x - 3)` for `y` in the first equation and solve for `x`:

`color(red)(-3x - 3) = 4x - 3`

`color(red)(-3x - 3) + color(blue)(3x + 3) = 4x - 3 + color(blue)(3x + 3)`

`color(red)(-3x) + color(blue)(3x) - color(red)(3) + color(blue)(3) = 4x + color(blue)(3x) - 3 + color(blue)(3)`

`0 - 0 = 4x + color(blue)(3x) - 0`

`0 = 4x + color(blue)(3x)`

`0 = (4 + 3)x`

`0 = 7x`

`0/color(red)(7) = (7x)/color(red)(7)`

`0 = (color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7))`

`0 = x` or `x = 0`

Now that we have `x` we can substitute `0` for `x` in the second equation and calculate `y`:

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

`y = 0 - 3`

`y = -3`