1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up 1. y = x + 2 2. y = x – 3 3. y = 2x + 3 4. y = x2
Graph each equation.
1. y = x + 2
2. y = x – 3
3. y = 2x + 3
4. y = x2

3. Problem of the Day
Write equations in slope-intercept form for a set of parallel lines. Then write two equations in slope-intercept form for two intersecting lines.
Possible answers:
parallel: y = 3x + 4 and y = 3x + 2
intersecting: y = x + 5 and y = 2x

4. Learn to graph systems of linear equations to find their solutions.

5. Additional Example 1: Graphing a System of Linear Equations by Graphing
A fishing boat leaves the harbor traveling east at 16 knots (nautical miles per hour). After it travels 40 nautical miles, a Coast Guard cutter follows the boat, traveling at 26 knots. After how many hours will the Coast Guard Cutter catch up with the fishing boat?
Let t = time in hours
Let d = distance in nautical miles
Fishing boat distance: d = 16t + 40
Coast Guard cutter distance: d = 26t

6. Additional Example 1 Continued
Graph each equation. The point of intersection appears to be (4, 104).
Check
d = 16t + 40
104 = 16(4) + 40 ?
104 = 104 
d = 26t
104 = 26(4) ?
104 = 104 
The Coast Guard cutter will catch up after 4 hours, 104 nautical miles from the harbor.

7. Check It Out: Example 1
A bus leaves the school traveling west at 50 miles per hour. After it travels 15 miles, a car follows the bus, traveling at 55 miles per hour. After how many hours will the car catch up with the bus?
Let t = time in hours
Let d = distance in miles
bus distance: d = 50t + 15
car distance: d = 55t

8. Check It Out: Example 1 Continued
Graph each equation. The point of intersection appears to be (3, 165).
Check
d = 50t + 15
200
165 = 50(3) + 15 ?
150
Distance (mi)
165 = 165 
100 50
d = 55t
165 = 55(3) ?
Time (h)
165 = 165 
The car will catch up after 3 hours, 165 miles from the school.

9. Not all systems of linear equations have graphs that intersect in one point. There are three possibilities for the graph of a system of two linear equations, and each represents a different solution set.

11. Additional Example 2A: Solving Systems of Linear Equations by Graphing
y = 2x – 7
3x + y = 3
Step 1: Solve both equations for y.
3x + y = 3
y = 2x – 7
–3x –3x
y = 3 – 3x
Step 2: Graph.
The lines intersect at (2, –3), so the solution is (2, –3).

12. Additional Example 2A Continued
Check
y = 2x – 7
3x + y = 3 ?
–3 = 2(2) – 7
3(2) + (–3) = 3 ? ?
–3 = –3 
3 = 3  ?

13. Additional Example 2B: Solving Systems of Linear Equations by Graphing
2x + y = 9
y – 9 = –2x
Step 1: Solve both equations for y.
2x + y = 9
y – 9 = –2x
–2x –2x
y = –2x + 9
y = –2x + 9
Step 2: Graph.
The lines are the same, so the system has infinitely many solutions.

14. Additional Example 2B Continued
Check
y = y ?
–2x + 9 = –2x + 9 ?
+2x x ?
9 = 9 

15. Check It Out: Example 2
y = –4x + 1
5x + y = –1
Step 1: Solve both equations for y.
y = –4x + 1
5x + y = –1
–5x –5x
y = –5x – 1
Step 2: Graph.
The lines are intersect at (–2, 9), so the solution is (–2, 9).

16. Check It Out: Example 2 Continued
y = –4x + 1
5x + y = –1 ?
9 = –4(–2) + 1
5(–2) + (9) = –1 ? ?
9 = 9 
–1 = –1  ?

17. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 17 17

18. Lesson Quiz
Solve each system of equations by graphing. Check your answer.
1. A car left Cincinnati traveling 55 mi/h. After it had driven 225 miles, a second car left Cincinnati on the same route traveling 70 mi/h. How long after the 2nd car leaves will it reach the first car?
15 h
2. y = x; y = 3x
(0, 0)
3. y = 4 – x; x + y = 1
no solution

19. Lesson Quiz for Student Response Systems
1. Solve the system of equations.
y = 2 – x
2y = 4 – 2x
A. no solution
B. infinitely many solutions
C. (1, 1)
D. (2, 2) 19 19

20. Lesson Quiz for Student Response Systems
2. Solve the system of equations.
y = 5 – x
3 – x = y
A. no solution
B. infinitely many solutions
C. (3, 5)
D. (5, 3) 20 20

21. Lesson Quiz for Student Response Systems
3. Solve the system of equations.
y = 5 – 2x
3x = y
A. no solution
B. infinitely many solutions
C. (1, 3)
D. (3, 1) 21 21