Question

How do you solve the following system?: `4x -12y =-3 , -3x +y = 18`

Answer 1

See entire solution process below:

Explanation:

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

`-3x + y = 18`

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

`0 + y = 18 + 3x`

`y = 3x + 18`

Step 2) Substitute `3x + 18` for `y` in the first equation and solve for `x`:

`4x - 12y = -3`

`4x - 12(3x + 18) = -3`

`4x - 36x - 216 = -3`

`-32x - 216 = -3`

`-32x - 216 + color(red)(216) = -3+ color(red)(216)`

`-32x - 0 = 213`

`-32x = 213`

`(-32x)/color(red)(-32) = 213/color(red)(-32)`

`(color(red)(cancel(color(black)(-32)))x)/cancel(color(red)(-32)) = -6.65625`

`x = -6.65625`

Step 3) Substitute `-6.65625` for `x` into the solution for `y` in the second equation in Step 1 and calculate `y`:

`y = 3x + 18`

`y = (3 xx -6.65625) + 18`

`y = -19.96875 + 18`

`y = -1.96875`

The solution is: `x = -6.65625` and `y = -1.96875`