# How do you solve the system 3x + 6y = 30 and x + 6y = 20?

Apr 8, 2017

Solve by elimination to find:

$x = 5 \text{ }$ and $\text{ } y = \frac{5}{2}$

#### Explanation:

Given:

$\left\{\begin{matrix}3 x + 6 y = 30 \\ x + 6 y = 20\end{matrix}\right.$

To eliminate the term in $y$, we can subtract the second equation from the first to get:

$2 x = 10$

and hence:

$x = 5$

Substituting this value of $x$ in the second equation, we get:

$5 + 6 y = 20$

Subtract $5$ from both sides to get:

$6 y = 15$

Divide both sides by $6$ to get:

$y = \frac{15}{6} = \frac{5}{2}$