Question

How do you solve the system of equations `-x - 3y = - 8` and `- 2x - 4y = - 10`?

Answer 1

See a solution process below:

Explanation:

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

`-x - 3y = -8`

`-x - 3y + color(red)(3y) = -8 + color(red)(3y)`

`-x - 0 = -8 + 3y`

`-x = -8 + 3y`

`color(red)(-1) xx -x = color(red)(-1)(-8 + 3y)`

`x = (color(red)(-1) xx -8) + (color(red)(-1) xx 3y)`

`x = 8 - 3y`

Step 2) Substitute `(8 - 3y)` for `x` in the second equation and solve for `y`:

`-2x - 4y = -10` becomes:

`-2(8 - 3y) - 4y = -10`

`(-2 * 8) + (-2 * -3y) - 4y = -10`

`-16 + 6y - 4y = -10`

`-16 + (6 - 4)y = -10`

`-16 + 2y = -10`

`color(red)(16) - 16 + 2y = color(red)(16) - 10`

`0 + 2y = 6`

`2y = 6`

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

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = 3`

`y = 3`

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

`x = 8 - 3y` becomes:

`x = 8 - (3 * 3)`

`x = 8 - 9`

`x = -1`

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