# How do you solve using elimination of 2x+5y=17 and 6x-5y=-9?

Nov 5, 2015

Add the equations to eliminate y and solve for x, and then substitute back to solve for y

#### Explanation:

Starting with
$\left\{\begin{matrix}2 x + 5 y = 17 \\ 6 x - 5 y = - 9\end{matrix}\right.$

We wish to solve for one of the variables by eliminating the other with addition or subtraction.
Note that we have $5 y$ in the first equation and $- 5 y$ in the second. This means we may eliminate the variable $y$ without further manipulation (in a more complicated case, we may need to first multiply both sides of one of the equations by a constant).
To do this, we can add the second equation to the first.

$\left(2 x + 5 y\right) + \left(6 x - 5 y\right) = 17 + \left(- 9\right) \implies 8 x = 8$

Dividing both sides by 8 gives $x = 1$.

Then we simply substitute our result for $x$ into either of the original equations. For example, using the first one gives
$2 \left(1\right) + 5 y = 17 \implies 5 y = 15 \implies y = 3$

So the solution is $\left\{\begin{matrix}x = 1 \\ y = 3\end{matrix}\right.$