Question

How do you solve this system of equations: `2x + 4y = - 8; 2x + 7y = - 20`?

Answer 1

See a solution process below:

Explanation:

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

`2x + 4y = -8`

`(2x + 4y)/color(red)(2) = -8/color(red)(2)`

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

`x + 2y = -4`

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

`x + 0 = -4 - 2y`

`x = -4 - 2y`

Step 2) Substitute `(-4 - 2y)` for `x` in the second equation and solve for `y`:

`2x + 7y = -20` becomes:

`2(-4 - 2y) + 7y = -20`

`(2 xx -4) - (2 xx 2y) + 7y = -20`

`-8 - 4y + 7y = -20`

`-8 + (-4 + 7)y = -20`

`-8 + 3y = -20`

`-8 + color(red)(8) + 3y = -20 + color(red)(8)`

`0 + 3y = -12`

`3y = -12`

`(3y)/color(red)(3) = -12/color(red)(3)`

`y = -4`

Step 3) Substitute `-4` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = -4 - 2y` becomes:

`x = -4 - (2 xx -4)`

`x = -4 - (-8)`

`x = -4 + 8`

`x = 4`

The Solution Is:

`x= 4` and `y = -4`

Or

`(4, -4)`