Question

How do you solve the system of equations `3x + y = - 6` and `10x + 10y = 20`?

Answer 1

See the entire solution process below:

Explanation:

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

`3x + y = -6`

`-color(red)(3x) + 3x + y = -color(red)(3x) - 6`

`0 + y = -3x - 6`

`y = -3x - 6`

Step 2) Substitute `-3x - 6` for `y` in the second equation and solve for `x`:

`10x + 10y = 20` becomes:

`10x + 10(-3x - 6) = 20`

`10x + (10 xx -3x) - (10 xx 6) = 20`

`10x - 30x - 60 = 20`

`-20x - 60 = 20`

`-20x - 60 + color(red)(60) = 20 + color(red)(60)`

`-20x - 0 = 80`

`-20x = 80`

`(-20x)/color(red)(-20) = 80/color(red)(-20)`

`(color(red)(cancel(color(black)(-20)))x)/cancel(color(red)(-20)) = -4`

`x = -4`

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

`y = -3x - 6` becomes:

`y = (-3 xx -4) - 6`

`y = 12 - 6`

`y = 6`

The solution is: `x = -4` and `y = 6` or `(-4, 6)`