Solving Systems of Linear Equations by Graphing Unit Exam Key

5

Solve It! Two professional downhill skiers average speeds throughout the race are shown in the diagram. Skier 1 starts 8 s before Skier 2. The course is 7000 ft long. Will Skier 2 pass Skier 1?

10

Solve It! How do you know?

10

Define system of linear equations.

10

Define solution of a system of linear equations.

1

Using your graph paper, find the solution of of the system at left

10

Describe the process of solving a system of linear equations by graphing.

10

Using your graph paper, find the solution of of the system at left

1

Find the solution to the following system of equations: y = 4x +7, y = 3x + 7

1

Find the solution to the following system of equations: y = (3x+2) + 5, y = 3x + 5

1

Find the solution to the following system of equations: y + 2 = 4(x-3), y + 2 = 1/5(x-3)

1

Find the solution to the following system of equations: y = 2x +2, y = 3(x +1)

10

Three types of systems are listed in the column on the right.
Drag the appropriate characteristic(s) from the left column to each type of system on the right.

has no solution
has exactly one solution
has infinitely many solutions

Inconsistent system
Consistent & independent system
Consistent & dependent system

1

Find the solution to the following system of equations: y - 3 = 5x + 4, y = 5x + 7

1

Find the solution to the following system of equations: y = 2x +6, y = 2x + 4

1

Reasoning: Before graphing the equations, how can you determine whether a system of equations has exactly one solution, infinitely many solutions, or no solution? In other words, how can you tell what type of system it is by looking at the equations?

1

Graph an example of a consistent system of linear equations. Zoom and pan your graph to establish an appropriate viewing window. Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

1

Identify the solution(s) of the system by graphing.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

1

Identify the solution(s) of the system by graphing.
Be sure to label scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

1

Identify the solution(s) of the system by graphing.
Be sure to include scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

1

Identify the solution(s) of the system by graphing.
Be sure to include scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Solve It! Two professional downhill skiers average speeds throughout the race are shown in the diagram. Skier 1 starts 8 s before Skier 2. The course is 7000 ft long. Will Skier 2 pass Skier 1?

Solve It! How do you know?

Define system of linear equations.

Define solution of a system of linear equations.

Using your graph paper, find the solution of of the system at left

Describe the process of solving a system of linear equations by graphing.

Using your graph paper, find the solution of of the system at left

Find the solution to the following system of equations: y = 4x +7, y = 3x + 7

Find the solution to the following system of equations: y = (3x+2) + 5, y = 3x + 5

Find the solution to the following system of equations: y + 2 = 4(x-3), y + 2 = 1/5(x-3)

Find the solution to the following system of equations: y = 2x +2, y = 3(x +1)

Three types of systems are listed in the column on the right. Drag the appropriate characteristic(s) from the left column to each type of system on the right.

Find the solution to the following system of equations: y - 3 = 5x + 4, y = 5x + 7

Find the solution to the following system of equations: y = 2x +6, y = 2x + 4

Reasoning: Before graphing the equations, how can you determine whether a system of equations has exactly one solution, infinitely many solutions, or no solution? In other words, how can you tell what type of system it is by looking at the equations?

Graph an example of a consistent system of linear equations. Zoom and pan your graph to establish an appropriate viewing window. Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Identify the solution(s) of the system by graphing. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Identify the solution(s) of the system by graphing. Be sure to label scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Identify the solution(s) of the system by graphing. Be sure to include scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Identify the solution(s) of the system by graphing. Be sure to include scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Three types of systems are listed in the column on the right.
Drag the appropriate characteristic(s) from the left column to each type of system on the right.

Identify the solution(s) of the system by graphing.
Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Identify the solution(s) of the system by graphing.
Be sure to label scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Identify the solution(s) of the system by graphing.
Be sure to include scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.

Identify the solution(s) of the system by graphing.
Be sure to include scale on both axes, Tell if the system is independent and consistent, inconsistent, or dependent and consistent.