Solving Systems of Equations by Graphing

Solving Systems of Equations by Graphing

​8.EE.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

We can solve thesystem of equation by graphing each equation and finding their intersection point. (Practice using Desmos)

• y = 2x + 3

• y = -3x + 4. What is the solution?

​8.EE.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Multiple Choice

What form do we need the equations to be in so that we can graph them?

• Standard From

• Slope-Intercept Form

• Point-Slope Form

• Any Form

One Solution



What does it mean if the systems of equations only have one solution?

​8.EE.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

No Solution

What does is mean when the systems of equations have no solution?

​8.EE.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Infinite Solutions

What does it mean when the systems of equations of an infinite amount of solutions?

​8.EE.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Multiple Choice

If you graph 2 lines and they intersect at ONE point, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None of These

Multiple Choice

If 2 lines never intersect, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None Of These

Multiple Choice

If a system has 2 lines that overlap, meaning they share all of the same points, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None Of These

Multiple Choice

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE
• FALSE

Multiple Choice

What is the first step in solving a system by graphing?

• Write both linear equations in slope-intercept form
• Get x by itself
• Compare the slopes of both equations
• Write both equations in standard form

Multiple Choice

A system of linear equations is... 

• Math Magic
• One Equation
• Always more than 2 equations
• A set of 2 or more equations

Multiple Choice

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Multiple Choice

How many solutions will this system have?

• One
• Two
• No Solution
• Infinitely Many Solutions

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution. 
• you will have one solution.
• you will have infinite solutions. 
• you will graph a giraffe. 

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Multiple Choice

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution
• No solution
• Infinitely Many Solutions

Multiple Choice

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

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

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