SLE - Solve Systems of Equations Graphically (Lesson)

Solve Systems of Equations Graphically

Let's think back on our two different cell phone plans:

You can tell from the table and the graph that the cost of each plan is $45 when you use 6GB of data. Let's write linear equations for each of the functions. We will write the functions using x and y, then we will write using function notation.

Now, let's graph these functions on the same coordinate plane.

Solving Systems of Equations Graphically Practice

Use the graph above to answer the questions below:

1. Initially which plan is cheaper? Which part of the equation helps you to know this?
2. Graphically, which plan has the greatest rate of change? Which part of the equation helps to determine this?
3. What does the point where the lines intersect represent?
4. What is the domain of both functions and why?

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

A system of equations is a set of two or more equations that use the same variables. An example looks like this:

y = 2x - 5

3x - y = 7

One of the ways you can solve systems of equations is by graphing. The solution to a system of equations is the ordered pair that is a solution for all of the equations in the system.

Here is the graph of these equations. We can see that the lines intersect at (2, -1). This is the solution, and the one ordered pair that satisfies both equations. We can verify this by plugging the coordinates into each equation to check:

Equation One

• y = 2x - 5
• -1 = 2(2) - 5
• -1 = 4 - 5
• -1 = -1

Equation Two

• 3x - y = 7
• 3(2) - (-1) = 7
• 6 + 1 = 7
• 7 = 7

Watch this video to see a few more examples!

Note that there are three different options for how lines can intersect, which means that there are three different types of answers you might give.

Graphing Systems of Equations

Graphing Systems of Equations Practice

Try these problems to see if you've got it: Rollover the equations for the solution.

1. Is (1, -3) a solution to the system of equations: y = 4x + 3 and y = -x - 2 

2. Is (2, 2) a solution to the system of equations: y = 3x - 4 and y = -(1/2)x + 3 

3. On your own paper, graph the system of equations and identify the solution: y = -x + 1 and y = (1/3)x - 3 

4. On your own paper, graph the system of equations and identify the solution: 6x + y = -3 and x + y = 2 

5. On your own paper, graph the system of equations and identify the solution: 2x + 3y = -9 and y = -x - 2 

6. On your own paper, graph the system of equations and identify the solution:

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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