## SAT SUBJECT TEST MATH LEVEL 1

## ALGEBRA

## CHAPTER 6

Equations and Inequalities

### SYSTEMS OF LINEAR EQUATIONS

A ** system of equations** is a set of two or more equations involving two or more variables. A solution consists of a value for each variable that will simultaneously satisfy each equation.

The equations 2*x* + *y* = 13 and 3*x* – *y* = 12 each have infinitely many solutions. A few of them are given in the tables that follow.

2*x* + *y* = 13

3*x* – *y* = 12

However, only one pair of numbers, *x* = 5 and *y* = 3, satisfies both equations simultaneously: 2(5) + 3 = 13 and 3(5) – 3 = 12. This then is the only solution of the system of equations:

Since the graphs of 2*x* + *y* = 13 and 3*x* – *y* = 12 are lines (see Chapter 13), these equations are called linear equations. You can use three basic methods to solve systems of linear equations, two algebraic ones—the addition method and the substitution method—and one graphic one.