Trouble on understanding an answer--please help, thanks!

[mlovering456]

What is the value of x?

(1) x + 2y = 4

(2) 5x + y + 15 = 3x - 3y + 23

The answer is E--but I don't understand why it cannot be C? Since I can find the value for Y in the first equation and plug it into the second equation (or vice versa) thus yielding the value for x-- The answer explanation did not address this possible solution--thanks in advance for the help!

[jssaggu.tico]

(1) x + 2y = 4

Statement 1: It's insufficient because of 2 variables in one equation. 'x' can't be extracted. So, eliminate A and D.

(2) 5x + y + 15 = 3x - 3y + 23
=> 5x-3x+y+3y = 23-15
=> 2x+4y = 8
=> x+2y = 4 (Same as eqn in statement 1)

Statement 2: It's insufficient because of 2 variables in one equation. 'x' can't be extracted. So, eliminate B.

Both together can't be used to solve because both equations are identical. Hence, no solution.

E is the answer.

[tim]

Thanks navjot. Remember, if you want to prove something insufficient, all you have to do is find two possibilities for an answer. If you have two identical linear equations, then x can take on literally any real value. Try it for yourself if you don’t see that..