How do you solve the following system: 2x+7y=1, x+3y=-2 ?

Jul 17, 2016

We use the value of $x$ in one equation and substitute in the other

Explanation:

Let's consider the second equation (the first would be the same but with this one is a little easier):

$x + 3 y = - 2$, this means that $x = - 3 y - 2$. Now substituting $x$ in the first equation we have:

$2 \left(- 3 y - 2\right) + 7 y = 1$, and then distributing $- 6 y - 4 + 7 y = 1$. So:

$y - 4 = 1$, and then $y = 5$. Using this value of $y$ in the second equation now we know:

$x = - 3 y - 2$, so $x = - \left(3 \cdot 5\right) - 2 = - 17$

You should always check that your answers are right by replacing the values you find in the given equations