Algebra and Trigonometry, 5th Edition

9.1 Systems of Equations in Two Variables

• Solve a system of two linear equations in two variables by graphing.

• Solve a system of two linear equations in two variables using the substitution method and the elimination method.

• Use systems of two linear equations to solve applied problems.

A system of equations is composed of two or more equations considered simultaneously. For example,

$$\begin{array}{ccccc}\hfill x& -& y& =& 5,\\ \hfill 2x& +& y& =& 1\end{array}$$

is a system of two linear equations in two variables. The solution set of this system consists of all ordered pairs that make both equations true. The ordered pair $\left(2,-3\right)$ is a solution of the system of equations above. We can verify this by substituting 2 for x and $-3$ for y in each equation.

GRAPHS OF EQUATIONS

REVIEW SECTION 1.1

Solving Systems ...