What is the value of x?

[VJesus12]

What is the value of \(x?\)

(1) \(5x + 3y = 15\)
(2) \(y = 5 - \frac{5}{3}x\)

[spoiler]OA=E[/spoiler]

Source: Magoosh

[Brent@GMATPrepNow]

What is the value of \(x?\)

(1) \(5x + 3y = 15\)
(2) \(y = 5 - \frac{5}{3}x\)

Target question: What is the value of x?

Statement 1: 5x + 3y = 15
Since this is a linear equation with infinitely many solutions. Here are two:
Case a: x = 3 and y = 0. In this case, the answer to the target question is x = 3
Case b: x = 0 and y = 5. In this case, the answer to the target question is x =0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y = 5 - (5/3)x
It looks like this equation MIGHT be the same as the equation for statement 1. Let's check....
Take: y = 5 - (5/3)x
Multiply both sides by 3 to get: 3y = 15 - 5x
Add 5x to both sides to get: 5x + 3y = 15
Since statement 2 provides the SAME information as statement 1, we can see that statement 2 is also NOT SUFFICIENT

Statements 1 and 2 combined
Whenever two statements provide the SAME information, the correct answer is either D or E.
In this case, the answer is obviously E

Cheers,
Brent