Question

How do you solve the system of equations `4x - 6y = - 8` and `2x - 2y = - 4`?

Answer 1

See a solution process below:

Explanation:

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

`2x - 2y = -4`

`2x - 2y + color(red)(2y) = -4 + color(red)(2y)`

`2x - 0 = -4 + 2y`

`2x = -4 + 2y`

`(2x)/color(red)(2) = (-4 + 2y)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -4/color(red)(2) + (2y)/color(red)(2)`

`x = -2 + y`

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

`4x - 6y = -8` becomes:

`4(-2 + y) - 6y = -8`

`(4 xx -2) + (4 xx y) - 6y = -8`

`-8 + 4y - 6y = -8`

`-8 + (4 - 6)y = -8`

`-8 + (-2)y = -8`

`-8 - 2y = -8`

`color(red)(8) - 8 - 2y = color(red)(8) - 8`

`-2y = 0`

`(-2y)/color(red)(-2) = 0/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 0`

`y = 0`

Step 3) Substitute `0` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = -2 + y` becomes:

`x = -2 + 0`

`x = -2`

The Solution Is: `x = -2` and `y = 0` or `(-2, 0)`