Question

For the following system of equations, what is the x-value of the solution `-x+2y=6, 6y=x+18`?

Answer 1

`x = 0`

Explanation:

Step 1) Solve the first equation for `y`:

`-x + 2y = 6`

`-x + color(red)(x) + 2y = 6 + color(red)(x)`

`0 + 2y = 6 - x`

`2y = 6 - x`

`(2y)/color(red)(2) = (6 - x)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 6/2 - x/2`

`y = 3 - x/2`

Step 2) Substitute `3 - x/2` for `y` in the second equation and solve for `x`:

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

`18 - (6x)/2 = x + 18`

`18 - 3x = x + 18`

`18 - 3x + color(red)(3x) - color(blue)(18) = x + 18 + color(red)(3x) - color(blue)(18)`

`18 - color(blue)(18) - 3x + color(red)(3x) = x + color(red)(3x) + 18 - color(blue)(18)`

`0 - 0 = 4x + 0`

`0 = 4x`

`0/color(red)(4) = (4x)/color(red)(4)`

`0 = (color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4))`

`0 = x`

`x = 0`