1. Graphing Calculator Lesson #2
Solving Systems of Equations on the Calculator

2. Finding the Intersection of Two Graphs
Set your viewing window to standard by pressing Zoom and then #6
Graph y = 3x – 2 in y1
Graph y = (1/2)x + 3 in y2
Press 2nd Calc (TRACE)
Press #5 for “intersect”
Press ENTER to confirm the first curve
Press ENTER to confirm the second curve
Press ENTER through the GUESS
You should see (2, 4) at the bottom
CASIO
Set your viewing window to STD by pressing SHIFT F3 and then choosing F3 for STD
Graph y = 3x – 2 in y1
Graph y = (1/2)x + 3 in y2
Press F5 for G-Solve
Choose F5 again for ISCT
You should see (2,4) at the bottom

3. You try one… Using the steps you just practiced, find the solution to…
y = 3x – 5
y = (1/3)x – 1
Compare your answer with a neighbor and write it down on your group sheet.

4. Solving for y
Notice that for both models of calculator, you have to have the equations solved for y before you can enter them into the calculator. So if your equations are in standard form, you will need to rearrange them first. Be careful when you enter them. Parentheses must be in the correct locations!
Example: Solve the system 2x – 4y = 8 and 4x + 2y = 5
2x – 4y = 8 4x + 2y =5
-4y = 8 – 2x y = 5 – 4x
y = (8 – 2x)/(-4) y = (5 – 4x)/2
Enter these into your calculator and find where they intersect.

5. Other types of systems….
Lines will only intersect at one point, but other types of systems may have more than one point of intersection. This means they have more than one solution.
On your calculator graph
y = -2x + 1
y = x2 – 2 (there is a shortcut button for squaring labeled x2)
How many points of intersection do you see?

6. Finding multiple points of intersection
Press 2nd Calc (TRACE) and choose #5 as before
Using the left/right arrow keys to move your cursor close to one of the points
Hit Enter three times to confirm the curves and get the intersection
Write down the point of intersection
Press 2nd Calc (TRACE) again and choose #5
Using the left/right arrow keys, move the cursor close to the OTHER point of intersection
Hit enter 3 times to get the intersection and write down the point
You should get (-3,7) and (1, -1)
CASIO
Press F5 for G-Solve and choose F5 for ISCT
One point of intersection should automatically appear. Write it down.
Use the left/right arrow keys to move to the other point of intersection and write it down.
You should get (-3,7) and (1.-1)

7. On your own….
!.) Find the solutions to the system: y = (1/4)x – 6 and y = -x2 + 2
They will be “ugly” decimals. Round to two decimal places. Compare answers with other members of your group and write them down on your group sheet.
2.) Solve this system…
y = 3x – 4
3x + 6y = 2
The answer will be an “ugly” decimal. Round to two decimal places. Compare your answer with your group and write it down on the group sheet.