Question

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

1. List item

Answer 1

See the entire solution process below:

Explanation:

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

`x + y = 6`

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

`x + 0 = 6 - y`

`x = 6 - y`

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

`x - y = 4` becomes:

`(6 - y) - y = 4`

`6 - y - y = 4`

`6 - 2y = 4`

`-color(red)(6) + 6 - 2y = -color(red)(6) + 4`

`0 - 2y = -2`

`-2y = -2`

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

`(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = 1`

`y = 1`

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

`x = 6 - y` becomes:

`x = 6 - 1`

`x = 5`

The solution is `x = 5` and `y = 1` or `(5, 1)`