Solving Systems of Equations By Graphing

Multiple Choice

Which of the following best describes a system of equations?

• A set of equations with different variables

• A set of equations with the same variables

• A single equation with multiple variables

• A set of equations with no variables

Multiple Select

Select all statements that are true about coinciding lines.

• They have the same slope.

• They have the same y-intercept.

• They have infinitely many solutions.

• They never intersect.

Open Ended

Explain the difference between parallel lines and coinciding lines in terms of their slopes and y-intercepts.

Multiple Choice

Which type of lines have exactly one solution when graphed?

• Intersecting lines

• Parallel lines

• Coinciding lines

• Vertical lines

Open Ended

Given the equations 2x + y = 4 and x - y = 2, what are the x- and y-intercepts for each equation?

Multiple Choice

Solve by graphing. Show all work on a graph paper.

• (2, 7)
• (7,6)
• (-6,1)
• No Solution

Multiple Choice

What is the solution to this system? 

• (3,1)
• No solution
• Infinite solutions
• (1,3)

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Multiple Choice

Where do the lines 2x + y = 4 and x - y = 2 intersect?

• (0, 4)

• (2, 0)

• (0, -2)

• (4, 2)

Multiple Choice

When checking your answer for a system of equations, what should you do if the point does not satisfy both equations?

• Change the equations

• Try a different point

• Recalculate the solution

• Ignore the result

Open Ended

Explain why two lines with the same slope but different y-intercepts have no solution when solving a system of equations by graphing.

Multiple Choice

Which of the following systems of equations has infinitely many solutions?

• y = 2x - 3 and y = 2x + 1

• 3x - y = 8 and 2y = 6x - 16

• x - y = 2 and 2x + y = 4

• y = 2x - 3 and -2x + y = 1

Open Ended

What are the three steps to solving a system of equations by graphing?

Multiple Choice

Which step involves substituting the x and y values into both equations to verify the solution when solving a system by graphing?

• Graph both equations

• Do the graphs intersect?

• Check your solution

• Label the solution

Open Ended

How confident do you feel about solving systems of equations by graphing after this lesson? What would you like to learn more about?

Multiple Choice

What is a system of equations?

• A set of equations with different variables

• A set of equations with the same variables

• A single equation with two variables

• A set of unrelated equations