Question

How do you solve the system of equations: `4x + 2y = 14` and `4x + 3y = 6`?

Answer 1

`x = 15/2` and `y = -8`

Explanation:

Step 1) First solve the second equation for `y` while keeping both sides of the equation balanced:

`4x + 2y = 14`

`4x + 2y - 4x = 14 - 4x`

`2y = 14 - 4x`

`(2y)/2 = (14 - 4x)/2`

`y = 7 - 2x`

Step 2) Substitute `7 - 2x` for `y` in the first equation and solve for `x` while keeping both sides of the equation balanced:

4x + 3(7 - 2x) = 6#

`4x + 21 - 2x = 6`

`2x + 21 = 6`

`2x + 21 - 21 = 6 - 21`

`2x = -15`

`(2x)/2 = 15/2`

`x = 15/2`

Step 3) Substitute `15/2` for `x` in the solution for Step 1 to find `y`:

`y = 7 - 2(15/2)`

`y = 7 - 15`

`y = -8`