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

May 28, 2018

$x = 3 , y = 2$

#### Explanation:

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

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

$\textcolor{b l u e}{x = 11 - 4 y}$

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

$2 \left(11 - 4 y\right) + 3 y = 12$

Distributing the $2$, we get

$22 - 8 y + 3 y = 12$

Combining like terms, we get

$22 - 5 y = 12$

We can subtract $22$ from both sides to get

$- 5 y = - 10$

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

$x = 11 - 4 \left(2\right)$

$x = 11 - 8$

$x = 3$

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

Hope this helps!