Question

How do you solve the system of equations `2x + 4y = - 20` and `3x + 5y = - 24`?

Answer 1

See a solution process below:

Explanation:

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

`2x + 4y = -20`

`(2x + 4y)/color(red)(2) = -20/color(red)(2)`

`(2x)/color(red)(2) + (4y)/color(red)(2) = -10`

`x + 2y = -10`

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

`x + 0 = -10 - 2y`

`x = -10 - 2y`

Step 2) Substitute `(-10 - 2y)` for `x` in the second equation and solve for `y`:

`3x + 5y = -24` becomes:

`3(-10 - 2y) + 5y = -24`

`(3 xx -10) - (3 xx 2y) + 5y = -24`

`-30 - 6y + 5y = -24`

`-30 + (-6 + 5)y = -24`

`-30 + (-1)y = -24`

`-30 - y = -24`

`color(red)(30) - 30 - y = color(red)(30) - 24`

`0 - y = 6`

`-y = 6`

`color(red)(-1) xx -y = color(red)(-1) xx 6`

`y = -6`

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

`x = -10 - 2y` becomes:

`x = -10 - (2 xx -6)`

`x = -10 - (-12)`

`x = -10 + 12`

`x = 2`

The solution is: `x = 2` and `y = -6` or `(2, -6)`