Question

How do you solve the system of equations: `y = 3x + 1` and `4x + y = 8`?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y`, we can substitute `(3x + 1)` for `y` in the second equation and solve for `x`:

`4x + y = 8` becomes:

`4x + (3x + 1) = 8`

`4x + 3x + 1 = 8`

`(4 + 3)x + 1 = 8`

`7x + 1 = 8`

`7x + 1 - color(red)(1) = 8 - color(red)(1)`

`7x + 0 = 7`

`7x = 7`

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

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 1`

`x = 1`

Step 2) Substitute `1` for `x` in the first equation and calculate `y`:

`y = 3x + 1` becomes:

`y = (3 * 1) + 1`

`y = 3 + 1`

`y = 4`

The solution is: `x = 1` and `y = 4` or `(1, 4)`