The Intersection of Graphs Method can be used to find approximate (sometimes exact) solutions to equations. Solve the equation 2x - 3 = x + 4 using this method.
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Intersection of Graphs Method of Solving an Equation

This method uses graphing of functions to solve an equation. 

STEP 1: Set Y sub 1 equal to the left side of the equation and Y sub 2 equal to the right side of the equation.

STEP 2: Graph Y sub 1 and Y sub 2 in the same viewing rectangle. 

STEP 3: Locate any points of intersection.  The set of x-values of these points of intersection corresponds to the solution set of the equation. Some solutions may be exact, while others may be only approximate solutions.

 

STEP 1: Press the button. Then enter the left side of the equation for Y sub 1 and the right side of the equation for Y sub 2.

Screen Picture of TI-83 Calculator

STEP 2: Next press ZOOM, then 6. This graphs the function in a Standard Window as shown below.

Screen Picture of TI-83 Calculator

STEP 3: The intersection point of the two lines is not visible using a standard window. Zoom out once so that the intersection point is visible.  (Remember to press ENTER for the zoom out to happen).  Now press the 2nd key, then TRACE [Calc], then select 5:intersection.

Screen Picture of TI-83 Calculator Screen Picture of the TI-83 Calculator


If the cursor is not near the intersection point, move it close to the point of intersection using the ARROW keys and then press ENTER.

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator


When Second curve? appears press ENTER again.   When Guess? appears press ENTER one more time.

Screen Picture of TI-83 Calculator Screen Picture of TI-83 Calculator
Screen Picture of TI-83 Calculator


The final screen shows that the intersection point is (7,11). If there are more points of intersection, move the cursor near each one and repeat the process. The X value of the intersection point, X = 7, is the solution to the equation. Notice that this is an exact solution.



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