Thinking Mathematically

Algebra: Graphs, Functions and Linear Systems

7.3 Systems of Linear Equations In Two Variables

Systems of Linear Equations and Their Solutions

• Two linear equations in two variables are called a system of linear equations.

• A solution to a system of linear equations is the set of ordered pairs which satisfy both equations.

• A system of linear equations may have– no solutions– 1 solution– Infinite solutionsWhat does this mean graphically?

Examples

• Checking a solution to a system of equationsExercise Set 7.3 #3

Determine if (2,5) is a solution to the system

2x + 3y = 17

x + 4y = 16

Examples• Solving a system by graphing

Exercise Set 7.3 #9Solve by graphing, check the solution

y = x + 5

y = -x + 3

Examples

• Solving a system by substitutionExercise Set 7.3 #15

Solve by substitution , check the solution

x + 3y = 8

y = 2x - 9

• Solving a system by addition method.Exercise Set 7.3 #27

Solve by the addition method , check the solution

2x + 3y = 6

2x – 3y = 6

More Examples

Exercise Set 7.3 #23, 37Solve by both methods

x + 8y = 6

2x + 4y = -3

Solve by either methodx = 9 - 2y

x + 2y = 13

Thinking Mathematically

Algebra: Graphs, Functions and Linear Systems

7.3 Systems of Linear Equations