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

1 Answer
Jacob
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.

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