Cracking The SAT Premium

Here’s an example:

If  4x  +   y   =   14  and 3x  +   2y  =   13, then    x   −   y   =   ?

Here’s How to Crack It

You’ve been given two equations here. But instead of being asked to solve for a variable (x or y), you’ve
been asked to solve for an expression (x − y). Why? Because there must be a direct solution.

In math class, you’re taught to solve one equation for one variable in terms of a second variable and to
substitute that value into the second equation to solve for the first variable.

Forget it. These methods are far too time consuming to use on the SAT, and they put you at risk of making
mistakes. There’s a better way. Just stack them on top of each other, and then add or subtract the two
equations; either addition or subtraction will often produce an easy answer. Let’s try it.

Adding the two equations gives you this:

Unfortunately, that doesn’t get us anywhere. So, try subtracting:

4 x +   y   =   14

3 x +   2y  =   13

When you subtract equations, just change the signs of the second equation and add. So the equation above
becomes

The value of (x − y) is precisely what you are looking for, so the answer is 1.

You can also use this method to solve problems in which you are asked to solve for an expression and
gives you fewer equations than variables. If you have dealt with simultaneous equations in your math
classes you may know that that puts you in a bind since it may be impossible to solve for each individual
variable.

Here is an example: