Question

How do you solve the system of equations `4x - 3y = - 4` and `y = - x + 6`?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the second equation is already solved for `y` we can substitute `(-x + 6)` for `y` in the first equation and solve for `x`:

`4x - 3y = -4` becomes:

`4x - 3(-x + 6) = -4`

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

`4x - (-3x) - 18 = -4`

`4x + 3x - 18 = -4`

`(4 + 3)x - 18 = -4`

`7x - 18 = -4`

`7x - 18 + color(red)(18) = -4 + color(red)(18)`

`7x - 0 = 14`

`7x = 14`

`(7x)/color(red)(7) = 14/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 2`

`x = 2`

Step 2) Substitute `2` for `x` in the second equation and calculate `y`:

`y = -x + 6` becomes:

`y = -2 + 6`

`y = 4`

The solution is: `x = 2` and `y = 4` or `(2, 4)`