How do you solve the following system: x-5y=-9, y = 3x – 12?

Mar 26, 2018

You have to substitute (replace) one of the unknowns into the other equation

Explanation:

We know that $x - 5 y = - 9$, so from here we have:

$x = 5 y - 9$. Substituting in the other equation we have:

$y = 3 x - 12 = 3 \left(5 y - 9\right) - 12 = 15 y - 27 - 12 = 15 y - 39$, and then:

$y + 39 = 15 y$, and so $39 = 14 y$, and then $y = \frac{39}{14}$

We can now use that $x = 5 y - 9$, so we have $x = 5 \cdot \frac{39}{14} - 9 = \frac{195}{14} - 9 = \frac{195 - 126}{14} = \frac{69}{14}$

The solutions are then $x = \frac{69}{14} , y = \frac{39}{14}$