7.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Solve Linear Systems by Graphing

7.1 Warm-Up 1. Graph the equation –2x + y = It takes 3 hours to mow a lawn and 2 hours to trim hedges. You spend 16 hours doing yard work. What are 2 possible numbers of lawns you mowed and hedges you trimmed? ANSWER 2 lawns and 5 hedges, or 4 lawns and 2 hedges

7.1 Example 1 SOLUTION Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1 3x – 2y = 5 Equation 2 The lines appear to intersect at the point (3, 2).

7.1 Example 1 ANSWER Because the ordered pair (3, 2) is a solution of each equation, it is a solution of the system. 7 = 7 CHECK Substitute 3 for x and 2 for y in each equation. x + 2y = (2) = ? 7 3x – 2y = 5 5 = 5 3(3) – 2(2 ) 5 = ?

7.1 Example 2 Solve the linear system : –x + y = –7 Equation 1 x + 4y = –8 Equation 2 SOLUTION STEP 1 Graph both equations. STEP 2 Estimate the point of intersection. The two lines appear to intersect at (4, – 3).

7.1 Example 2 STEP 3 Check whether (4, –3) is a solution by substituting 4 for x and –3 for y in each of the original equations. Equation 1 –x + y = –7–x + y = –7 –7 = –7 –(4) + (–3) –7 = ? Equation 2 x + 4y = –8x + 4y = –8 –8 = – (–3) –8 = ? ANSWER Because (4, –3) is a solution of each equation, it is a solution of the linear system.

7.1 Guided Practice Solve the linear system by graphing. Check your solution. –5x + y = x + y = 10 ANSWER (1, 5) 2x + y = 4 –x + 2y = 3 2. ANSWER (1, 2) 3x + y = 3 x – y = 5 3. ANSWER (2, –3)

7.1 Example 3 As a season pass holder, you pay $4 per session to use the town’s tennis courts. Without the season pass, you pay $13 per session to use the tennis courts. The parks and recreation department in your town offers a season pass for $90.

7.1 Example 3 Which system of equations can be used to find the number x of sessions of tennis after which the total cost y with a season pass, including the cost of the pass, is the same as the total cost without a season pass ? y = 13x y = 4x A y = 13x y = x C y = 4x y = x B y = x y = x D

7.1 Example 3 SOLUTION Write a system of equations where y is the total cost (in dollars) for x sessions. EQUATION 1 y = 13 x

7.1 Example 3 y = x ANSWER The correct answer is C. A C B D EQUATION 2

7.1 Guided Practice 4. Solve the linear system in Example 3 to find the number of sessions after which the total cost with a season pass, including the cost of the pass, is the same as the total cost without a season pass. ANSWER 10 sessions 5. WHAT IF? In Example 3, suppose a season pass costs $135. After how many sessions is the total cost with a season pass, including the cost of the pass, the same as the total cost without a season pass? ANSWER 15 sessions

7.1 Example 4 A business rents in-line skates and bicycles. During one day, the business has a total of 25 rentals and collects $450 for the rentals. Find the number of pairs of skates rented and the number of bicycles rented. RENTAL BUSINESS

7.1 Example 4 SOLUTION STEP 1 Write a linear system. Let x be the number of pairs of skates rented, and let y be the number of bicycles rented. x + y = 25 15x + 30y = 450 Equation for number of rentals Equation for money collected from rentals STEP 2 Graph both equations.

7.1 Example 4 STEP 3 Estimate the point of intersection. The two lines appear to intersect at (20, 5). STEP 4 Check whether (20, 5) is a solution = ? 15( 20 ) + 30(5) 450 = ? 450 = = 25 ANSWER The business rented 20 pairs of skates and 5 bicycles.

7.1 Guided Practice In Example 4, suppose the business has a total of 20 rentals and collects $420. Find the number of bicycles rented. 6. ANSWER 8 bicycles

7.1 Lesson Quiz Use the graph to solve the linear system. 1. 3x – y = 5 –x + 3y = 5 ANSWER (2, 1) 2. Solve the linear system by graphing. 2x + y = –3 –6x + 3y = 3 ANSWER (–1, –1)

7.1 Lesson Quiz ANSWER A pet store sells angel fish for $6 each and clown loaches for $4 each. If the pet store sold 8 fish for $36, how many of each type of fish did it sell ? 3. 2 angel fish and 6 clown loaches