Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write...

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Example 1 Number of Solutions Example 2 Solve a System of Equations Example 3 Write and Solve a System of Equ ations

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Transcript of Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write...

Page 1: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Example 1 Number of Solutions

Example 2 Solve a System of Equations

Example 3 Write and Solve a System of Equations

Page 2: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Graphing Systems of Equations

• Two equations together are called a system of equations.

• A solution of a system of equations is an ordered pair of numbers that satisfies both equations.

• A system of two linear equations can have 0, 1, or an infinite number of solutions.

Page 3: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

System of Equations

InconsistentConsistent

Parallel lines, no solutions

Dependent(an infinite number of

solutions, the equations graph the same line)

Independent(exactly one solution,

graphs intersect at a single point)

Page 4: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.
Page 5: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Use the graph to determine whether the system has no solution, one solution, or infinitely many solutions.

Answer: Since the graphs of andare parallel, there are no solutions.

Page 6: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Use the graph to determine whether the system has no solution, one solution, or infinitely many solutions.

Answer: Since the graphs of andare intersecting lines, there is one solution.

Page 7: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Use the graph to determine whether the system has no solution, one solution, or infinitely many solutions.

Answer: Since the graphs of andcoincide, there are infinitely many solutions.

Page 8: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Use the graph to determine whether each system has no solution, one solution, or infinitely many solutions.

a.

b.

c.

Answer: one

Answer: no solution

Answer: infinitely many

Page 9: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Graphing Linear EquationsWrite the equation in Slope-Intercept Form:

y = mx +b, where m is the slope and b is the y-intercept

1.Solve for y (get everything on the other side of the equal sign)

2.Begin with “b” – graph the y-intercept

3.From the y-intercept, use the slope (rise/run) to find your second point.

4.Draw your line and label with the equation.

Page 10: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

The graphs of the equations coincide. There are infinitely many solutions of this system of equations.

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

Answer:

Page 11: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

The graphs of the equations are parallel lines. Since they do not intersect, there are no solutions of this system of equations.

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

Answer:

Page 12: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

a.

Answer:one; (0, 3)

Page 13: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Answer:no solution

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.

b.

Page 14: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Bicycling Tyler and Pearl went on a 20-kilometer bike ride that lasted 3 hours. Because there were many steep hills on the bike ride, they had to walk for most of the trip. Their walking speed was 4 kilometers per hour. Their riding speed was 12 kilometers per hour. How much time did they spend walking?

Words You have information about the amount of time spent riding and walking. You also know the rates and the total distance traveled.

Variables Let the number of hours they rode andthe number of hours they walked. Write a

system of equations to represent the situation.

Page 15: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Equations

The number ofhours riding plus

the number ofhours walking equals

the total number of hours of the trip.

The distancetraveled riding plus

the distancetraveled walking equals

the total distance of the trip.

r + w = 3

12r + 4w = 20

Page 16: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Graph the equations and .

The graphs appear to intersect at the point with the coordinates (1, 2). Check this estimate by replacing r with 1 and w with 2 in each equation.

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Check

Answer: Tyler and Pearl walked for 3 hours.

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Alex and Amber are both saving money for a summer vacation. Alex has already saved $100 and plans to save $25 per week until the trip. Amber has $75 and plans to save $30 per week. In how many weeks will Alex and Amber have the same amount of money?

Answer: 5 weeksnumber of weeksamount of money saved

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Page 20: Lesson 1 Contents Example 1Number of Solutions Example 2Solve a System of Equations Example 3Write and Solve a System of Equations.

Assignment

• Page 372: 15-22, 25-37 odd


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