Question

How do you solve `3x+4y=-4` and `x+2y=2` using substitution?

Answer 1

See the entire solution process below:

Explanation:

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

`x + 2y = 2`

`x + 2y - 2y = 2 - 2y`

`x + 0 = 2 - 2y`

`x = 2 - 2y`

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

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

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

`6 - 2y = -4`

`6 - 6 - 2y = -4 - 6`

`0 - 2y = -10`

`-2y = -10`

`(-2y)/color(red)(-2) = (-10)/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 5`

`y = 5`

Step 3) Substitute `color(red)(5)` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = 2 - (2 xx color(red)(5))`

`x = 2 - 10`

`x = -8`

The solution is:

`x = -8` and `y = 5` or (-8, 5)