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.

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

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.


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.


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


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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