Question

When solving the system of equations by graphing, what is the solution of 3x + 2y = 2 and 2x – y=6?

A (-2,2)
B. (2.-2)
C. (-2,-2)
D. (2, 2)

Answer 1

answer B: (2,-2)

Explanation:

First, write the equations on top of each other:

`3x+2y=2\\2x-y=6`

Then, multiply the the second equation by 2 so that we can use elimination of the y-variable:

`3x+2y=2\\2(2x-y)=2(6)\\\\3x+2y=2\\4x-2y=12`

Next, use elimination to find the value of "x":

`3x+2y=2\\+(4x-2y=12)\\\\7x+0=14\\7x=14\\(7x)/(7)=(14)/(7)\\x=2`

So, your x-value is 2.

Now, substitute your x-value into one of your equations, let's take the second equation, 2x-y=6:

`2x-y=6\\2(2)-y=6\\4-y=6\\4-4-y=6-4\\-y=2\\(-y)/(1)=(2)/(-1)\\y=-2`

Your y-value is -2.

With all your information gathered, you find that the solution to this system of equation is (2,-2).