Question

What is the value of x in the solution to the following system of equations?

x − 2y = 2
3x + y = 6

Answer 1

Do you have any idea where to start?

Answer 2

x - 2y = 2 --> x = 2y + 2
now sub 2y + 2 in for x in the other equation
3x + y = 6
3(2y + 2) = 6
6y + 6 = 6
6y = 6 - 6
6y = 0
y = 0/6 = 0
now sub 0 in for y
x - 2y = 2
x - 2(0) = 2
x - 0 = 2
x = 2
check...
3x + y = 6
3(2) + 0 = 6
6 + 0 = 6
6 = 6 (correct)
ANSWER : (2,0)

Answer 3

Do you have any questions...if so, please ask them

Answer 4

This is the substitution method....it can also be solved by using the elimination method

Answer 5

3x + y = 6
3(2y + 2) = 6 <--- should be 3(2y+2) + y = 6 # the '+y' is gone.

Otherwise, it is good.

Answer 6

I messes up.....let me do it again
x - 2y = 2 --> x = 2y + 2
now sub 2y + 2 in for x in the other equation
3x + y = 6
3(2y + 2) + y = 6 (distribute through the parenthesis)
6y + 6 + y = 6 (combine like terms)
7y + 6 = 6
7y = 6 - 6
7y = 0
y = 0/7 = 0
x is solved the same way ...in the above answer I did.
It doesn't make a difference in the answer because y is still 0.
thanks @franciscanmonk for finding my mistake :)

Answer 7

No probs. I didn't really check if it would make a difference though. haha.

Answer 8

I kinda freaked out....I thought I just gave the wrong answer....when I re-did it, I found that it wouldn't have made a difference.

Answer 9

It's all good. Don't worry :)

Answer 10

That is, it wouldn't have made a difference in the answer. But if you had to show your work, that would be a problem.....

Answer 11

You're right. :)