Using Substitution

To solve for two variables in an equation, it is possible to use substitution once more is known about one variable in the equation. This answer would then be used to find the final answer that the SAT math question is asking for on the test. If you need to solve for two variables, you can substitute information you know about one variable to help solve a second equation. Substitution Example 1 Here is a simple example of a substitution problem that may appear on the math section of the SAT. Remember that sometimes equations look more complicated than they are in reality.  If x = 20 and y = 10, what will be the value of 5x (x - y)? To solve this it is simply necessary to substitute the values for x and y to get the number the question wants. So, for this example 5•20(20 - 10) = 1000 Example Problem 2 If no numbers are given but there is more than one equation on the math section of the SAT test, it is a good idea to choose one equation to begin with and solve for the variable in that equation. Then, the next step is to substitute the answer from the first equation into the second equation.  Here is an example:  If 4x = 12 and 7x + 2y = 25, what is y? The first step is to start with the easier equation. For this question, it would be 4x = 12. The answer will be x= 3 at the end. This number should then be plugged into the second equation in the question.  7•3 + 2y =25 21 + 2y = 25 2y = 4 y = 2 There should always be one equation for each variable that needs to be solved in a question. Occasionally the equation will be simple (like 4x = 12) although at other times it can be quite a bit more complicated. In complicated cases, the equation may have a variable in the answer, which is okay. It is simply a matter of taking that and plugging it into the second equation to get the final answer.  This method of solving for two variables in a question is referred to as substitution.  Occasionally, it is possible to use elimination to solve these problem, which we will go into in a later section of this website.  Overall, as with other sections of the SAT math section, it is important to read the question carefully before attempting to get an answer.