# How do you solve the system of equations y= 3x - 2 and y = 2x - 8?

Jun 10, 2017

$x = - 6$ and $y = - 20$

#### Explanation:

To solve this system of equations, you can use a method called substitution, where you put $y$ in terms of $x$, and replace $y$ in the other equation for $y$ in terms of $x$. You can also do this with $x$ in terms of $y$.

Fortunately, both are already in terms of $y$.

$y = 3 x - 2$ and $y = 2 x - 8$, so because $y = y$: $3 x - 2 = 2 x - 8$.

Then by subtracting $2 x$ off each side:

$3 x - 2 - 2 x = 2 x - 8 - 2 x \implies x - 2 = - 8$

And adding $2$ to each side:

$x - 2 + 2 = - 8 + 2 \implies x = - 6$

So we have the value of $x$, which we can put back into the equation for $y$ in terms of $x$:

$y = 3 x - 2 = 3 \times - 6 - 2 = - 20$, hence our value for $y$.

You can then check this by putting the values into the two original equations and making sure they add up.