Question

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

Answer 1

See the entire solution process below:

Explanation:

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

`2x + y = 3`

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

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

`0 + y = 3 - 2x`

`y = 3 - 2x`

Step 2) Substitute `3 - 2x` for `y` in the first equation and solve for `x`:

`3x + 2y = 4` becomes:

`3x + 2(3 - 2x) = 4`

`3x + (2 xx 3) - (2 xx 2x) = 4`

`3x + 6 - 4x = 4`

`3x - 4x + 6 = 4`

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

`-1x + 6 = 4`

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

`-x + 0 = -2`

`-x = -2`

`color(red)(-1) xx -x = color(red)(-1) xx -2`

`x = 2`

Step 3) Substitute `2` for `x` in the solution to the second equation at the end of Step 1 and calculate `y`:

`y = 3 - 2x` becomes:

`y = 3 - (2 xx 2)`

`y = 3 - 4`

`y = -1`

The solution is `x = 2` and `y = -1` or `(2, -1)`