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

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

Then by subtracting 2x off each side:

3x-2-2x=2x-8-2x => x-2=-8

And adding 2 to each side:

x-2+2=-8+2 => x=-6

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

y = 3x-2=3xx-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.