# How do you solve the system of equations 5x - 3y = 1 and 9x - 4y = 6?

Apr 24, 2018

$x = \frac{16}{7}$
$y = \frac{73}{21}$

#### Explanation:

Firstly, you have to multiply each equation so there is the same number of a letter in each equation. In this case it is easier to make both $y$s equal $12$.
$5 x - 3 y = 1$ should be multiplied by 4
#20x - 12y = 4

$9 x - 4 y = 6$ should be multiplied by 3
$27 x - 12 y = 18$

You can then take one equation away from the other. I will take the first away from the second:
$27 x - 12 y = 18$
$20 x - 12 y = 4$ $-$
$\left(27 x - 20 x\right) + \left(- 12 y - - 12 y\right) = 18 - 4$
$7 x = 16$
$x = \frac{16}{7}$

You can then put this value of $x$ into one of the original equations to get a value for $y$:
$\left(5 \times \frac{16}{7}\right) - 3 y = 1$
$3 y = \frac{80}{7} - 1$
$3 y = \frac{73}{7}$
$y = \frac{73}{21}$