Question

How do you solve the system of equations `y= 1x+4` and `y=8x-3`?

Answer 1

See the entire solution process below:

Explanation:

Because the first equation is already solved for `y`, substitute `1x + 4` for `y` in the second equation and solve for `x`:

`1x + 4 = 8x - 3`

`1x + 4 - color(red)(1x) + color(blue)(3) = 8x - 3 - color(red)(1x) + color(blue)(3)`

`1x - color(red)(1x) + 4 + color(blue)(3) = 8x - color(red)(1x) - 3 + color(blue)(3)`

`0 + 7 = 7x - 0`

`7 = 7x`

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

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

`1 = x`

`x = 1`

Step 2) Substitute `1` for `x` in the first equation and calculate `y`:

y = (1 xx 1) + 4#

`y = 1 + 4`

`y = 5`

The solution is:

`x = 1` and `y = 5`