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MATH IN DEMAND

Solving Systems of Equations
by Graphing

How do we solve a systems of equations by graphing?
We can solve a systems of equations by graphing each linear equation on the same graph.  The point of intersection between the two graphs is the solution.

As seen earlier, there are 3 types of solutions.  When graphing the systems of equations, they will either have one solution, no solutions, or infinitely many solutions.
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Now in order to graph the linear equations, we want the equations to be in slope-intercept form.  This means that we want "y" to be solved in each equation. Once each equation is in slope-intercept form (y = mx + b), then we can graph the equations and identify the solution(s).

​Let's look at some examples:

Example #1

Solve the systems of equations by graphing:
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The first thing that I notice from the system of equations is that both equations are in slope-intercept form
(y is solved for in both equations).  This means that I can go straight to graphing each equation.
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Example #2

Solve the systems of equations by graphing:
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Now, in this systems of equations I notice that both equations are NOT in slope-intercept form (y is not solved for in both equations).  This means that I need to solve for y in each equation before I can graph the system of equations.
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Practice

Solve the following systems of equations by graphing:
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Click here to check your answer.
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(C) 2017 MATH IN DEMAND​