If 2x+y=4 and 2x-y=8, then 3x-y=?
Can someone help me with a learning sequence to understand and solve this problem. I can't seem to follow the logic.
Many ways to go about it. Consider if you just add the two equations together:
2x + y = 4
2x - y = 8
4x = 12
Then solve for x, so x = 3. Plug that in to either of your original equations to find y.
An alternate solution method is to solve one of them for y. We'll use the top one:
y = 4 - 2x.
Now, take that value and put it in for y in the second one.
2x - (4 - 2x) = 8.
Simplifying that, we get
2x - 4 + 2x = 8
4x - 4 = 8
4x = 12
so x = 3.
You know y = 4 - 2x, so y = 4 - 6 = -2.
Thanks so much for the reply.
According to the GRE test prep, the answer they are looking for is 11.
The way the question is asked is what is confusing me. I solved for "x" as you illustrated.
If 2x+y=4 and 2x-y=8, then 3x-y=What
any thoughts ?
Immediately you know y is negative, since a change from adding y to 2x to subtracting y from 2x gives a larger number (from 4 to 8).
But then x must be positive. Since you cant add two negative numbers
(2x+y) and get a positive.
Since x is positive 3x > 2x, so 3x-y > 2x-y, and therefore the answer must be bigger than 8. There is only once such solution given: 3x-y = 11.