# How do you solve using elimination of -2x+3y=-5 and -x+6y=-1?

Nov 6, 2015

$y = \frac{1}{3} \mathmr{and} x = 3$ using elimination.

#### Explanation:

Elimination involves multiplying one equation to make two variable equal to each other.

When I (or you) look at this equation, we can look at either variable. What I notice is that I can multiply $3 y$ by $- 2$ to make them cancel eachother out.
$- 1 x + 6 y = - 1 \text{ } \implies - 1 x + 6 y = - 1$
$\left(- 2 x + 3 y = - 5\right) \left(- 2\right) \implies 4 x - 6 y = 10$

As you can can see above, I have lined by each $y$ with each other. We can add the top equation from the bottom equation. That will leave us with $3 x = 9$. We can simplify to $x = 3$.

Now we can plug $x$ into either equation to solve for y. I will use $- 1 x + 6 y = - 1$.

$- 1 \left(3\right) + 6 y = - 1$
$\text{ } - 3 + 6 y = - 1$
$\text{ } 6 y = 2$
$\text{ } y = \frac{1}{3} \mathmr{and} x = 3$