Question

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

Answer 1

See a solution process below:

Explanation:

Step 1) Because the second equation is already solved for `y` we can substitute `(x - 2)` for `y` in the first equation and solve for `x`:

`2x + 4y = 4` becomes:

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

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

`2x + 4x - 8 = 4`

`(2 + 4)x - 8 = 4`

`6x - 8 = 4`

`6x - 8 + color(red)(8) = 4 + color(red)(8)`

`6x - 0 = 12`

`6x = 12`

`(6x)/color(red)(6) = 12/color(red)(6)`

`(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) = 2`

`x = 2`

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

`y = x - 2` becomes:

`y = 2 - 2`

`y = 0`

The Solution Is:

`x = 2` and `y = 0`

Or

`(2, 0)`