Question

How do you solve `2x + 3y = 12` and `x + 4y = 11`?

Answer 1

`x=3, y=2`

Explanation:

Let's start with the second equation and solve for `x` in terms of `y`.

We can subtract `4y` from both sides to get

`color(blue)(x=11-4y)`

We have solved for `x` in terms of `y`, so we can plug this into the first equation. We get

`2(11-4y)+3y=12`

Distributing the `2`, we get

`22-8y+3y=12`

Combining like terms, we get

`22-5y=12`

We can subtract `22` from both sides to get

`-5y=-10`

Dividing both sides by `-5`, we get

`y=2`

To completely solve for `x`, we can go back to the equation I have in blue, and plug in `y=2`. We get

`x=11-4(2)`

`x=11-8`

`x=3`

Thus, `x=3` and `y=2`.

Hope this helps!