Question

How do you solve the following linear system?: `-6x+6y=6 , 2x+y=19`?

Answer 1

See the entire solution process below:

Explanation:

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

`-6x + 6y = 6`

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

`(-6x)/color(red)(6) + (6y)/color(red)(6) = 1`

`-x + y = 1`

`color(red)(x) - x + y = color(red)(x) + 1`

`0 + y = x + 1`

`y = x + 1`

Step 2) Substitute `x + 1` for `y` in the second equation and solve for `x`:

`2x + y = 19` becomes:

`2x + (x + 1) = 19`

`2x + x + 1 = 19`

`3x + 1 = 19`

`3x + 1 - color(red)(1) = 19 - color(red)(1)`

`3x + 0 = 18`

`3x = 18`

`(3x)/color(red)(3) = 18/color(red)(3)`

`x = 6`

Step 3) Substitute `6` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = x + 1` becomes:

`y = 6 + 1`

`y = 7`

The solution is: `x = 6` and `y = 7` or `(6, 7)`