## SAT SUBJECT TEST MATH LEVEL 1

## ALGEBRA

## CHAPTER 6

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: 4*x* + 2*y* = 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.