# How do you solve 8a+2b=11 and 5a-6b=25?

May 23, 2018

$a = 2 , b = - \frac{5}{2}$

#### Explanation:

We have the following system:

$8 a + 2 b = 11$

$5 a - 6 b = 25$

We want to eliminate one of the variables so we can solve for the other. So let's multiply the first system by $3$. We get

$24 a + 6 b = 33$

$5 a - 6 b = 25$

Now we can add both systems to get

$29 a = 58$

Dividing both sides by $29$, we get

$\textcolor{b l u e}{a = 2}$

We've solved for one of the variables, now we can plug into an equation to solve for the other.

I'll plug into the first equation. We get

$8 \left(2\right) + 2 b = 11$

which simplifies to

$16 + 2 b = 11$

$\implies 2 b = - 5$

$\implies \textcolor{b l u e}{b = - \frac{5}{2}}$

Now, we've solved for both of our variables.

Hope this helps!