# How do you solve the system using the elimination method for 3x - 4y = 9 and 2x + 3y = 7?

Jun 2, 2018

See below

#### Explanation:

We have two linear equations (to be solved by elimination method)

$3 x - 4 y = 9$
$2 x + 3 y = 7$

Multiply first eq. by $- 2$ and second by $3$

$- 6 x + 8 y = - 18$
$6 x + 9 y = 21$

Now we can add both equations and eliminate the unknown x

$17 y = 3$

$y = \frac{3}{17}$

$x$ can be found in first equation (for example)

3x-4·3/17=9
3x=9+4·3/17
$x = \frac{55}{17}$

Solution is the pair of values $\left(\frac{3}{17} , \frac{55}{17}\right)$