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Solving Simulataneous Equations Using a Calculator

It is possible to use a calculator to solve systems of equations. You do this by interpreting the solution as the point of intersection between the two lines.

Re-write equations as functions in the slope-intercept form

In order for the calculator to be able to interpret the equations, you first need to write them in the slope-intercept form, $y = mx + c.$ This means solving the equations for $y$ which then gives the functions for the two straight lines.

Enter the equations into the calculator

These functions now can to be entered into the calculator. On a TI-calculator this is done by first pressing "Y=" and then entering the function's expression on the lines $\text{Y}_1$, $\text{Y}_2$ and so forth. To write $x$, use the "X,T,$\theta$, n" button.

Draw the functions

When the functions have been entered, press the GRAPH button in order to draw them in the coordinate system.

In order to change the $x$- and $y$-values which the coordinate system is draw between, you can press the WINDOW button which contains the preferences for how the coordinate system should be displayed.

Find the intersection point

You can now use the calculator to find the point of intersection between the two graphs that were drawn. The tool that finds it is found by first pushing CALC (2nd + TRACE) and then choosing "5:intersect" from the list.

When you have chosen "5:intersect", the graphs will be drawn again and you need to choose from which two graphs you would like to determine the point of intersection.

• First curve: Choose the first graph by pressing ENTER. If there are more than two graphs, you can choose between them by using the up and down arrows.
• Second curve: Choose the other graph in the same way.
• Guess: In order for the calculator to be able to determine the point of intersection more quickly, it asks the user for a starting point. Place the marker near the point of intersection by using the left and right arrows and then hitting ENTER.

The point of intersection's $x$- and $y$-values are now displayed which is the solution for the simultaneous equations.