Solving Systems of equations by graphing

Open Ended

Describe a real-life situation where you might need to solve a system of equations. What would the intersection point represent in your example?

Multiple Choice

Why is it important to find the intersection point when solving systems of equations by graphing?

• Because it shows where the equations have the same solution

• Because it makes the graph look complete

• Because it helps to draw straight lines

• Because it is always at the origin

Multiple Choice

Which of the following is the correct order of steps to solve a system of equations by graphing?

• Rewrite equations in slope-intercept form, graph each line, identify the intersection point, check the solution

• Graph each line, rewrite equations in slope-intercept form, check the solution, identify the intersection point

• Identify the intersection point, graph each line, check the solution, rewrite equations in slope-intercept form

• Check the solution, identify the intersection point, graph each line, rewrite equations in slope-intercept form

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Multiple Choice

Given the equations y = 2x + 1 and y = -x + 4, what is the solution to the system when solved by graphing?

• The lines intersect at one point

• The lines are parallel

• The lines overlap completely

• There is no solution

Open Ended

Explain the difference between a system of equations that has no solution and one that has infinite solutions when graphed.

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Multiple Choice

Which of the following pairs of equations represents parallel lines?

• y = 2x + 1 and y = 2x - 3

• y = x + 2 and y = -x + 4

• y = x + 2 and y = x + 2

• y = 2x + 1 and y = -x + 4

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Fill in the Blanks

A system of equations where both equations are y = x + 2 will have

solutions.

Open Ended

Choose one of the practice problems and describe the steps you would take to solve it by graphing.

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Multiple Choice

At what value of x do the costs of Plan A and Plan B become equal based on their equations?

• x = 100

• x = 200

• x = 300

• x = 400

Multiple Select

Which of the following statements are true about systems of equations?

• A system can have one solution.

• A system can have no solution.

• A system can have infinitely many solutions.

• A system always has exactly two solutions.

Open Ended

Explain how graphing can help you find the solution to a system of equations, using the cell phone plan example.

Fill in the Blanks

The intersection point of the lines y = x + 2 and y = -x - 1 is at x =

Open Ended

Compare the graphs in Practice Graph 2 and Practice Graph 3. How does the difference in slopes affect the number and type of solutions for each system?

Fill in the Blanks

A system of equations is solved by finding the point where the lines

Open Ended

After learning about systems of equations and how to solve them by graphing, what questions do you still have or what would you like to explore further about this topic?

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