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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. 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? 3.1 – 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? 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! 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 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 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. 3.1 – Solve Linear Systems by Graphing 3.1 – Solve Linear Systems by Graphing Example 6: Solve the system. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 4x – 3y = 8 8x – 8y = 16 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