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Why is this concept useful?: Graphing a system of equations helps to visually show how the set of equations interacts with each other, and is another way of finding the solution to a system of equations.
Where does this concept fit into the curriculum?: Middle school

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What is graphing a system of equations?

Graphing a set of equations to visually see where the solution lies between the equations.

How to graph a system of equations:

Take the following set of equations:

\begin{array}{l} y=\frac{1}{2} x+3\\ y=x+1 \end{array}

First graph the first equation:

Then graph the second equation:

Wherever the two lines intersect, is where the solution of the two equations is.

In this case it is (4,5).

Sample Math Problems

1. Find the solution of the following graph:

Answer:
The solution is where the two lines intersect or (-4, 5)

2. Find the solution of the following graph:

Answer:
The solution is where the two lines intersect or (1,7).

3. How many solutions are in the system of equations shown below:

Answer:
There are no solutions as the following set of equations are parallel to each other

4. How many solutions are in the system of equations shown below:

Answer:
Infinite, as the two equations are the same line

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Practice Math Problems

1. Is it possible for a set of linear equations to have two solutions?

2. Graph the following equations and find the solution:

y=4x + 3

y= -x - 2

3. Graph the following equations and find the solution:

\begin{array}{l} y=-1\\ y=\frac{-5}{2} x+4 \end{array}

4. Graph the following equations and find the solution:

\begin{array}{l} y=-\frac{1}{2} x-1\\ y=\frac{1}{4} x-4 \end{array}

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Functions Worksheets

Graphing system of equations

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