1. 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

2. 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

3. 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.

4. 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.

5. 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

6. 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.

7. 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)

8. 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)

9. 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)

10. 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.

11. 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 = x B
y = 13x
y = x C
y = x
y = x D

12. 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 = x

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

14. 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

15. 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

16. 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.

17. 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.

18. 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. = ?
15(20) + 30(5) = ?
25 = 25
450 = 450
ANSWER
The business rented 20 pairs of skates and 5 bicycles.

19. 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

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

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

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

23. 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