IXL | Find the number of solutions to a system of equations by graphing

Graph these equations:

Click to select points on the graph.

Coordinate plane graph with 4 quadrants, x-axis coordinates from -10 to 10, y-axis coordinates from -10 to 10.

How many solutions does the system of equations have?

no solution

one solution

infinitely many solutions

ref_doc_title.

Learn with an example

question

Graph these equations:

–

Click to select points on the graph.

How many solutions does the system of equations have?

no solution

one solution

infinitely many solutions

key idea

A system of two equations can be classified as follows:

If the two lines are parallel, the system is inconsistent, with no solution.
If the two lines intersect at one point, the system is consistent and independent, with one solution.
If the two lines are the same, the system is consistent and dependent, with infinitely many solutions.

solution

The first equation is

–

The

-intercept

–

Plot the point

(

–

)

The slope is

–

Move down 2 and right 1 to find another point on the line.

Draw a line connecting them.

The second equation is

–

The

-intercept

–

Plot the point

(

–

)

The slope is 2. Move up 2 and right 1 to find another point on the line.

Draw a line connecting them.

Finally, identify the point of intersection.

The two lines intersect at one point. The system has one solution.

Looking for more? Try these:

Lesson: Systems of equations

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Questions
answeredQuestions

Time
elapsedTime

hr	min	sec
00	00	04

SmartScore
out of 100
IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the Challenge Zone to achieve mastery (100)! Learn more

Teacher tools

Work it out

Not feeling ready yet? These can help:

GG.2Solve a system of equations by graphing

M.20Find the number of solutions

Lesson: Systems of equations

Excellent! You got that right!

Jumping to level 1 of 1

Excellent!