How to Use a Graphing Calculator to Solve a Systems of Equations
Convert the equations into y= form In order to graph an equation on your calculator, the left side of the equation must only contain y., Plug the equations into your calculator., Make sure all plots are turned off and other equations cleared...
Step-by-Step Guide
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Step 1: Convert the equations into y= form In order to graph an equation on your calculator
This is pretty easy to do, especially if you are dealing with linear equations.
All you have to do is solve your equation for y.
If it is a linear systems in standard form (Ax+By=C), then you can just write down the following equation, subbing in for the constants A, B, and C: y=(c-ax)/b or you can use the second method.
If your equations are in slope intercept form, you already have the equation in y= form. -
Step 2: the left side of the equation must only contain y.
Press the y= button, usually the top left button on your calculator, and type in your first equation under y1 and your second equation under y2.
Since you can only use 2 variables with this method, you shouldn't need more than 2 equations.
If instead of y=, you have something else, make sure you are in function mode by pressing the mode button and making sure "Func" is highlighted. , On the TI83, plots that are turned on are highlighted in the y= menu.
If there are any on, simply move your cursor over them and press enter.
You should also scroll down on the y= screen to make sure there are no other equations set to graph.
If there are you have two options:
If you might need the equation later, move your cursor to the "=" sign and press enter to unselect it.
Only the entries with their "=" signs highlighted will graph, but your equation will still be entered if you need it.
To make the equation graph again, move your cursor onto the "=" sign again and press enter to highlight it.
If you won't need the equation later, move your cursor to the entry (not the "=" sign) and press clear.
You can't retrieve the equation if you do this, so be sure you want to clear it before you do this. , Guess at what your answer might be.
You want to be your answer is on the screen.
Press the "window" button, usually the button just to the right of the y= button.
The xmin should be considerably less than your guess and the xmax should be considerably higher.
Then, instead of worrying about your y=, just press the "zoom" button just to the right of the "window" button then scroll down to "ZoomFit" and press enter.
In a few seconds your graph should appear on the screen.
If you can't see the intersection of the graphs, adjust the window until you can. , Press "2nd" then "Trace" to bring you to the "Calculate" menu.
Scroll down to intersect and press enter.
It should prompt "First curve?" Make sure your cursor is on one of the graphs and press enter.
It should then prompt "Second curve?" Make sure your cursor is on the other graph and press enter.
It will prompt "Guess?" The easiest way to do this for equations that only intersect once is to press enter again.
If they intersect twice on the same page, either enter a value that is close to the x value where they intersect (You could use your estimated value for x in step 4) or move your cursor near where they intersect.
Remember: it doesn't have to be perfect; your calculator is just trying to make sure it finds the right intersection point for you.
It doesn't really need an accurate guess.
To navigate on the graph screen:
Press the up and down buttons to switch between graphs.
This will not change your x value.
Press the left and right buttons to move along the graph.
Your x value change will be incremental, your y change will be the output of the x value, so your cursor may move faster some times and slower others. , On the bottom of your screen, your calculator should say "x=a number" and "y=a number." These are your answers.
Copy them down to the desired accuracy. -
Step 3: Plug the equations into your calculator.
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Step 4: Make sure all plots are turned off and other equations cleared.
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Step 5: Choose an appropriate window.
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Step 6: Find the intersection of the graphs.
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Step 7: Write down your solution.
Detailed Guide
This is pretty easy to do, especially if you are dealing with linear equations.
All you have to do is solve your equation for y.
If it is a linear systems in standard form (Ax+By=C), then you can just write down the following equation, subbing in for the constants A, B, and C: y=(c-ax)/b or you can use the second method.
If your equations are in slope intercept form, you already have the equation in y= form.
Press the y= button, usually the top left button on your calculator, and type in your first equation under y1 and your second equation under y2.
Since you can only use 2 variables with this method, you shouldn't need more than 2 equations.
If instead of y=, you have something else, make sure you are in function mode by pressing the mode button and making sure "Func" is highlighted. , On the TI83, plots that are turned on are highlighted in the y= menu.
If there are any on, simply move your cursor over them and press enter.
You should also scroll down on the y= screen to make sure there are no other equations set to graph.
If there are you have two options:
If you might need the equation later, move your cursor to the "=" sign and press enter to unselect it.
Only the entries with their "=" signs highlighted will graph, but your equation will still be entered if you need it.
To make the equation graph again, move your cursor onto the "=" sign again and press enter to highlight it.
If you won't need the equation later, move your cursor to the entry (not the "=" sign) and press clear.
You can't retrieve the equation if you do this, so be sure you want to clear it before you do this. , Guess at what your answer might be.
You want to be your answer is on the screen.
Press the "window" button, usually the button just to the right of the y= button.
The xmin should be considerably less than your guess and the xmax should be considerably higher.
Then, instead of worrying about your y=, just press the "zoom" button just to the right of the "window" button then scroll down to "ZoomFit" and press enter.
In a few seconds your graph should appear on the screen.
If you can't see the intersection of the graphs, adjust the window until you can. , Press "2nd" then "Trace" to bring you to the "Calculate" menu.
Scroll down to intersect and press enter.
It should prompt "First curve?" Make sure your cursor is on one of the graphs and press enter.
It should then prompt "Second curve?" Make sure your cursor is on the other graph and press enter.
It will prompt "Guess?" The easiest way to do this for equations that only intersect once is to press enter again.
If they intersect twice on the same page, either enter a value that is close to the x value where they intersect (You could use your estimated value for x in step 4) or move your cursor near where they intersect.
Remember: it doesn't have to be perfect; your calculator is just trying to make sure it finds the right intersection point for you.
It doesn't really need an accurate guess.
To navigate on the graph screen:
Press the up and down buttons to switch between graphs.
This will not change your x value.
Press the left and right buttons to move along the graph.
Your x value change will be incremental, your y change will be the output of the x value, so your cursor may move faster some times and slower others. , On the bottom of your screen, your calculator should say "x=a number" and "y=a number." These are your answers.
Copy them down to the desired accuracy.
About the Author
Rachel Torres
Rachel Torres has dedicated 15 years to mastering lifestyle and practical guides. As a content creator, Rachel focuses on providing actionable tips and step-by-step guides.
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