How to Solve Simultaneous Equations Graphically
Solving for multiple equations at once using graphs is the easiest way to solve the system. The process to solve for many equations may be difficult for some at first. The process never changes, however, so after practicing once or twice, it gets much easier.
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Instructions
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1
Set each of your equations to "Y." To get "Y" alone on one side of each of your equations, you must use simple algebraic manipulations.
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2
Draw one large Cartesian coordinate system on your graph paper, or two perpendicular lines, representing your plane. It is on these axes you will draw your graph.
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3
Plug several numbers into one of your equations for X and solve for Y. Plot each (X,Y) point onto your coordinate system.
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4
Connect your points with a smooth line, once you have plotted 5 to 10 points for one equation. You may use a ruler if your graph is linear. Once you have drawn the graph for one equation, repeat Steps 3 and 4 until all of your equations are plotted and drawn on one coordinate.
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5
Record the point at which your graphs intersect, or cross, to solve your system of equations. This resulting point is the solution to your system.
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Tips & Warnings
If you don't want to go through the trouble of drawing your graphs, you may also use a graphic calculator, TI 83 and better recommended. To graph your equations, you must press the "Y=" button at the top left hand corner of the calculator. Record each equation in the calculator and press "Graph." To calculate the intersection of the lines, press calculate and scroll down to the option that says "Intersection." Press the "Equals" button three times, and the solution will appear and the lower left hand corner of your screen.
If your graphs do not intersect, there is no value that solves the system of the equations.
