IXL - Find the number of solutions to a system of equations by graphing (Algebra 1 practice)

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

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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 up 2 and right 3 to find another point on the line.

Draw a line connecting them.

The second equation is

–

The

-intercept

–

Plot the point

(

–

)

The slope is

Move up 2 and right 3 to find another point on the line.

Draw a line connecting them.

Finally, identify the point of intersection.

The two lines are the same. The system has infinitely many solutions.

Looking for more? Try these:

Lesson: Systems of equations

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Teacher tools

Work it out

Not feeling ready yet? These can help:

O.2Solve a system of equations by graphing

C.15Find the number of solutions to a linear equation

Lesson: Systems of equations

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