Substitution Questions
Substitution Questions
We like substitution questions. Not because they have great personalities and a really good sense of humor. We love ’em because they’re easy. They almost aren’t algebra at all. Substitutions give you an algebraic equation and then tell you the value of the variable. Just plug in that variable and work out the answer.
If 2y + 8x = 11, what is the value of 3(2y + 8x)?
You might see this equation bubbling over with variables and panic. Don’t. It’s simple. Since the question states that 2y + 8x = 11, and you’re looking for the value of 3(2y + 8x), all you have to do is substitute 11 for 2y + 8x in the expression, and you get 3(11) = 33.
Not many substitution questions on the SAT are this simple, though. For more complicated substitution questions, you’ll have to do some extra math either before or after the substitution.
Math Before Substitution
If 3x – 7 = 8, then 23 – 3x = ?
In this problem, you have to find what 3x equals before you can substitute that value into the expression 23 – 3x. To find 3x, take that first equation,
and add 7 to both sides, giving
Now substitute that 15 into 23 – 3x:
Math After Substitution
If a + b = 7 and b = 3, then 4a = ?
In this question, you have to plug the value for b into a + b = 7 in order to find a:
Once you know that a = 4, just substitute into 4a:
For substitution questions in which you have to plug in values in more than one stage, make sure you work out that last substitution. When you’re taking the SAT under real time pressure, you may be so consumed with getting to the next question that, for instance, you solve for a = 4 but then forget to substitute that value into 4a. SAT traps are waiting for you to do just that. Recognize that 4 is an imposter answer and defeat them.
Multiple Substitutions
There’s another type of substitution problem on the SAT that you’ll probably have to deal with: multiple substitutions. On these questions, you have to do more than one substitution. For instance,
If , y = 3x, and x = 2, then what is the value of z?
To approach this problem, you just have to substitute 2 for x to find y, and then substitute those values into the equation for z. Substituting 2 for x into y = 3x gives y = 3(2) = 6. Substituting for y and x in the equation for z, gives
Help | Feedback | Make a request | Report an error