solving systems of equations by graphing

Multiple Choice

Which of the following best describes the point of intersection when graphing two linear equations?

• It is where the two lines cross and represents the solution to both equations.

• It is where the lines are parallel and never meet.

• It is the midpoint of the two lines.

• It is the point farthest from the origin.

Open Ended

Why is it important to be able to solve systems of linear equations by graphing in real-life situations?

Multiple Choice

Which of the following best describes a system of linear equations?

• A set of two or more linear equations with the same variables

• A single linear equation

• A set of equations with different variables

• A set of nonlinear equations

Multiple Choice

What are the possible outcomes when two lines are graphed in a system of equations?

• One solution, no solution, or infinitely many solutions

• Only one solution

• Only no solution

• Only infinitely many solutions

Open Ended

Explain the steps you would take to solve a system of equations by graphing, using the example provided.

Multiple Choice

What is the intersection point of the lines y = x + 2 and y = -x?

• (1, 3)

• (0, 2)

• (2, 4)

• (2, 0)

Multiple Choice

Which points would you plot for the equation y = 2x + 1 based on the example?

• (-1,-1), (0,1), (1,3), (2,5)

• (0,4), (1,3), (2,2), (3,1)

• (-1,1), (0,0), (1,2), (2,4)

• (1,1), (2,2), (3,3), (4,4)

Open Ended

How confident do you feel about graphing linear equations and finding the point of intersection to solve a system? What would you like to know more about?

Open Ended

Create a system of linear equations that intersects at the point (2, 5).

Fill in the Blanks

The solution to the system of equations y = 2x + 1 and y = -x + 4 is

.

Multiple Choice

What are the two main objectives when learning to solve systems of linear equations by graphing?

• Graphing linear equations and solving by substitution

• Graphing linear equations and solving by elimination

• Graphing linear equations and solving by finding their point of intersection

• Graphing linear equations and factoring

Fill in the Blanks

One solution occurs when two lines

each other.

Open Ended

Why does the point (1, 3) satisfy both equations in the example?

Multiple Select

Which of the following statements are true about the solutions to a system of two linear equations?

• If the lines intersect, there is one solution.

• If the lines are parallel, there is no solution.

• If the lines are the same, there are infinite solutions.

• If the lines are perpendicular, there are infinite solutions.

Multiple Choice

What does it mean if two lines never intersect when solving a system of equations?

• No solution

• One solution

• Infinite solutions

• The lines are perpendicular

Multiple Choice

The solution to this system of equations is:

• (4, 3)
• (3, 4)
• (-4, 3)
• No solution

Multiple Choice

Is the following point a solution to the given system of equations?

(5,1)

y = -x + 6

y = 2x - 9

• Yes

• No

Multiple Choice

Is the following point a solution to the given system of equations?

(-1,-5)

y = -x + 2

y = 3x - 2

• Yes

• No

Multiple Choice

The solution to a system of equations is the place at which the lines ___________.

• intersect.

• have the same slope.

• have the same domain.

Multiple Choice

These two lines intersect at _____.

• (4, -2)
• (4, 2)
• (-2, 4) 
• No solution

Multiple Choice

The solution to this system of equations is:

• (4, 3)
• (3, 4)
• (-4, 3)
• No solution

Multiple Choice

Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-1, 4)
• (1, -4)
• (-4, 1)
• (4, -1)

Multiple Choice

Lesly graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-3,-8)
• (-8,-3)
• (3,-8)
• (8,3)

Multiple Choice

Which system of linear equations has no solution?

Multiple Choice

Which system of linear equations has infinite solutions?

Multiple Choice

Which system of equations has one solution?