candyandy wrote:

I have notice that it is often the case on DS case questions that the test writers will give you an equation with two variables as one condition. The other condition will give you one of the variables and you end up falling into the "C trap". Does anyone know if there is a way to tell that an equation with two variables has only one unique solution? If so, is there to quickly generate the solution besides simple guess and test? Thanks in advance.

If you have two linearly independent equations for two variables, you will be able to solve for both variables.

Linearly independent:

What is the value of \(x\)?

\(1) x+y=2\)

\(2) x+2y=3\)

The two equations are linearly independent because they are not equivalent. In other words, you are unable to transform either of the equations into another. Since we need 1) and 2) to get two linearly independent equations, we need both statements to be sufficient. Pick C.

Not linearly independent:

What is the value of \(x\)?

\(1) x+y=2\)

\(2) 2x+2y+3=7\)

You can subtract 3 from both sides in 2) to get \(2x+2y = 4\), and then divide both sides by 2 to get \(x+y=2\). This means that 2) is equivalent to 1), so we actually do not have two separate equations. Statements 1) and 2) combined are insufficient. Pick E.

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