1. Graph the equation –2x + y = 1. ANSWER 2. 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

Check the intersection point EXAMPLE 1 Check the intersection point Use the graph to solve the system. Then check your solution algebraically. x + 2y = 7 Equation 1 3x – 2y = 5 Equation 2 SOLUTION The lines appear to intersect at the point (3, 2). CHECK Substitute 3 for x and 2 for y in each equation. x + 2y = 7 3 + 2(2) = ? 7 7 = 7

Check the intersection point EXAMPLE 1 Check the intersection point 3x – 2y = 5 3(3) – 2(2) 5 = ? 5 = 5 ANSWER Because the ordered pair (3, 2) is a solution of each equation, it is a solution of the system.

Use the graph-and-check method EXAMPLE 2 Use the graph-and-check method Solve the linear system: –x + y = –7 Equation 1 x + 4y = –8 Equation 2 SOLUTION STEP 1 Graph both equations.

Use the graph-and-check method EXAMPLE 2 Use the graph-and-check method STEP 2 Estimate the point of intersection. The two lines appear to intersect at (4, – 3). 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 Equation 2 –x + y = –7 x + 4y = –8 –(4) + (–3) –7 = ? 4 + 4(–3) –8 = ? –7 = –7 –8 = –8

EXAMPLE 2 Use the graph-and-check method ANSWER Because (4, –3) is a solution of each equation, it is a solution of the linear system.

EXAMPLE 2 GUIDED PRACTICE Use the graph-and-check method for Examples 1 and 2 Solve the linear system by graphing. Check your solution. –5x + y = 0 1. 5x + y = 10 ANSWER (1, 5)

EXAMPLE 2 GUIDED PRACTICE Use the graph-and-check method for Examples 1 and 2 Solve the linear system by graphing. Check your solution. 2x + y = 4 –x + 2y = 3 2. ANSWER (1, 2)

EXAMPLE 2 GUIDED PRACTICE Use the graph-and-check method for Examples 1 and 2 Solve the linear system by graphing. Check your solution. 3x + y = 3 x – y = 5 3. ANSWER (2, –3)

EXAMPLE 3 Standardized Test Practice The parks and recreation department in your town offers a season pass for $90. • 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.

EXAMPLE 3 Standardized Test Practice 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 = 4x y = 90 + 13x B y = 13x y = 90 + 4x C y = 90 + 4x y = 90 + 13x D

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

Standardized Test Practice EXAMPLE 3 Standardized Test Practice EQUATION 2 y = 90 + 4 x ANSWER The correct answer is C. A C B D

GUIDED PRACTICE for Example 3 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

GUIDED PRACTICE for Example 3 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

EXAMPLE 4 Solve a multi-step problem RENTAL BUSINESS 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.

Solve a multi-step problem EXAMPLE 4 Solve a multi-step problem 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 Equation for number of rentals 15x + 30y = 450 Equation for money collected from rentals STEP 2 Graph both equations.

Solve a multi-step problem EXAMPLE 4 Solve a multi-step problem 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. 20 + 5 25 = ? 15(20) + 30(5) 450 = ? 25 = 25 450 = 450 ANSWER The business rented 20 pairs of skates and 5 bicycles.

EXAMPLE 4 Solve a multi-step problem GUIDED PRACTICE for Example 4 WHAT IF? 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

Warm-up: Homework: Page 372 # 3-5 all, #12-26 all, # 31, #33, #35

Daily Homework Quiz Use the graph to solve the linear system 1. 3x + y = 3 x – y = 5 ANSWER (2, –3)

Daily Homework Quiz 2. Solve the linear system by graphing. 2x + y = –3 –6x + 3y = 3 ANSWER (–1, –1)

Daily Homework Quiz 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. ANSWER 2 angel fish and 6 clown loaches