Algebra 1 6-1 Independent Practice: Solving Systems by Graphing

by Matthew Richardson

| 17 QuestionsComplete all of the graphing in this assignment by hand before checking your work using the embedded Desmos graphing calculator below. After checking your work, you may edit your own graphs.

1

20

Solve the system by graphing.

Work carefully and precisely to ensure that you graphs reveal the correct solution.

As always, check your solution using substitution.

2

10

Identify the solution to the system of equations you solved by graphing in the previous item.

Write your response in the following format, with a space immediately following the comma: (5, -4)

(0, 7)

(-3, 7)

(2, 5)

(6, 13)

3

20

Solve the system by graphing.

Work carefully and precisely to ensure that you graphs reveal the correct solution.

As always, check your solution using substitution.

4

10

Identify the solution to the system of equations you solved by graphing in the previous item.

Write your response in the following format, with a space immediately following the comma: (5, -4)

5

20

Solve the system by graphing.

Work carefully and precisely to ensure that you graphs reveal the correct solution.

As always, check your solution using substitution.

6

10

Identify the solution to the system of equations you solved by graphing in the previous item.

Write your response in the following format, with a space immediately following the comma: (5, -4)

7

20

Solve the system by graphing. Zoom and pan your graph to establish an appropriate viewing window.

8

10

Identify the solution to the system of equations you solved by graphing in the previous item.

Write your response in the following format, with a space immediately following the comma: (5, -4)

9

40

Concert Tickets: Tickets for a concert cost $10 each if you order them online, but you must pay a service charge of $8 per order. The tickets are $12 each if you buy them at the door on the night of the concert, with no service charge.

a. Write a system of equations to model the situation. Let c be the total cost. Let t be the number of tickets.

b. Graph the equations and find the intersection point.

10

10

Analysis: What does the intersection point of the system of equations you graphed in number 9 represent?

11

5

Vocabulary: How many solutions does an inconsistent system have?

exactly one

no solutions

infinitely many

12

5

Vocabulary: How many solutions does a consistent and dependent system have?

exactly one

no solutions

infinitely many

13

5

Vocabulary: How many solutions does an consistent and independent system have?

exactly one

no solutions

infinitely many

14

10

Writing: Suppose you graph a system of linear equations. If a point is on only one of the lines, is it a solution of the system? Explain.

No; A point must be on both lines to be a solution of the system.

Yes; As long as the point is on at least one line, it is a solution of the system.

15

10

Reasoning: Can a system of two linear equations have exactly two solutions? Explain.

No; Two lines can not intesect in exactly two places. They must intersect in 0, 1, or infinitely-many places (aka overlap one another). This means that a system of linear equations must have 0, 1, or infinitely-many solutions.

Yes; Two lines may intersect at exactly two places. This means that a system of equations may have exactly 2 solutions.

16

10

Reasoning: Suppose you find that two linear equations are true when x = -2 and y = 3. What can you conclude about the graphs of the equations? Explain.

You can conclude that the graphs of the linear equations will share the common point (-2, 3).

You can conclude that the graphs of the linear equations will have at least 2 points of intersection.

You can conclude that one of the graphs is a horizontal line and that the other is a vertical line.

17

10

Reflection: Math Success

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