Question

How do you solve this system of equations: `-6x + 6y = - 12;- 10x + 9y = - 17`?

Answer 1

See the entire solution process below:

Explanation:

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

`-6x + 6y = -12`

`(-6x + 6y)/color(red)(6) = -12/color(red)(6)`

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

`-x + y = -2`

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

`0 + y = x - 2`

`y = x - 2`

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

`-10x + 9y = -17` becomes:

`-10x + 9(x - 2) = -17`

`-10x + (9 * x) - (9 * 2) = -17`

`-10x + 9x - 18 = -17`

`-x - 18 = -17`

`-x - 18 + color(red)(18) = -17 + color(red)(18)`

`-x - 0 = 1`

`-x = 1`

`color(red)(-1) * -x = color(red)(-1) * 1`

`x = -1`

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

`y = x - 2` becomes:

`y = -1 - 2`

`y = -3`

The solution is: `x = -1` and `y = -3` or `(-1, -3)`