SAT SUBJECT TEST MATH LEVEL 1
Equations and Inequalities
THE ADDITION METHOD
EXAMPLE 27: The easiest way to solve the system of equations discussed above is to add the two equations:
Now solve for y by replacing x with 5 in either of the two original equations. For example:
So the unique solution is x = 5 and y = 3.
The addition method worked so nicely in Example 27 because adding the two equations eliminated the variable y. That does not always happen, however, as the following example illustrates.
EXAMPLE 28: To solve the system, you cannot just add the two equations.
Fortunately, there is an easy remedy. If you multiply the first equation by 2, you will get an equivalent equation: 4x + 2y = 26. Now you can use the addition method to solve the new system:
Then, substitute 4 for x in one of the original equations:
So the solution is x = 4 and y = 5.
In Example 29 below, you have to multiply each of the equations in a system by a different number to yield a new system in which adding the equations will eliminate a variable.
EXAMPLE 29: To solve the system, multiply the first equation by 3 and the second equation by –2, and then add the new equations:
Now replace y by 7 in either of the original equations:
The solution is x = 5 and y = 7.