1. 3.1 – Solve Linear Systems by Graphing A system of two linear equations in two variables x and y, also called a linear system, consists of two equations that can be written in the following form. Ax + By = C Dx + Ey = F A solution of a system of linear equations in two variables is an ordered pair that satisfies each equation.

2. 3.1 – Solve Linear Systems by Graphing Example 1: During one calender year, a state trooper issued a total of 375 citations for warnings and speeding tickets. Of these, there were 37 more warnings than speeding tickets. How many warnings and how many speeding tickets were issued?

3. 3.1 – Solve Linear Systems by Graphing Example 2: You worked 14 hours last week and earned a total of $96 before taxes. Your job as a lifeguard pays $8 per hour, and your job as a cashier pays $6 per hour. How many hours did you work at each job?

4. 3.1 – Solve Linear Systems by Graphing Example 3: A gym offers two options for membership plans. Option A includes an initiation fee of $121 and costs $1 per day. Option B has no initiation fee but costs $12 per day. After how many days will the total costs of the gym membership plans be equal? How does your answer change if the daily cost of Option B increases? Explain!

5. 3.1 – Solve Linear Systems by Graphing Example 4: Graph the linear system and estimate the solution. Then check the solution algebraically. 3x + 2y = -4 x + 3y = 1

6. 3.1 – Solve Linear Systems by Graphing Example 5: Graph the linear system and estimate the solution. Then check the solution algebraically. 4x – 5y = -10 2x – 7y = 4

7. 3.1 – Solve Linear Systems by Graphing A system that has at least one solution is consistent. If a system has no solution, the system is inconsistent. A consistent system that has exactly one solution is independent and a consistent system that has infinitely many solutions is dependent.

8. 3.1 – Solve Linear Systems by Graphing

9. Example 6: Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 4x – 3y = 8 8x – 8y = 16

10. 3.1 – Solve Linear Systems by Graphing Example 7: Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 2x + y = 4 2x + y = 1