Question

How do you solve `2x + 3y = 6` and `x + y = 3` using substitution?

Answer 1

`x = 3, y = 0`

Explanation:

`2x + 3y = 6`

`x + y = 3`

Let's solve for `x` in the second equation

`x = 3 - y`

Now let's plug `(3-y)` in for `x` in the first equation

`2(3-y) + 3y = 6`

`6 - 2y + 3y = 6`

`y = 0`

`* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *`

Now we have `y`, let's find `x`

`x = 3 - y`

`x = 3 - 0`

`x = 3`

`* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *`

Let's double check our work and use our `x` and `y` values in the first equation and solve it. If our numbers are correct, the equation should equal `6`

#2(3) + 3(0)

`6 + 0`

`6 = 6`! We were right!