You can solve this equation by algebraic methods or use option 5 from the CALCULATE menu. To use the calculator, enter 4x + 5 in Y1 and x - 2 in Y2 and then graph. To learn more about graphing on the calculator, click here.
You can see that the two graphs cross each other. You want to find out where. By pressing and choosing option 5, you will see the screen below.
The calculator is asking for the first curve. When you press , there will be a prompt for the second curve.
By pressing again, the calculator wants a guess.
You simply have to press one more time to see the answer.
When you solve the equation algebraically, you get the x–value that makes the equation true. So the x–value on the screen is the answer you need as the solution to the equation.
Notice that you did not have to do a lot of work to find the point of intersection in the last example. This is because there were only two "curves" (two things entered in the Y= screen) and one point of intersection.
This changes as the graphs become more complicated. Look at the equation 2x2 - 7 = x - 1. By using Y1 = 2x2 - 7 and Y2 = x - 1 and then graphing, you can see two points of intersection.
When you press and choose option 5, the calculator will again prompt you for a first and second curve. As in the last example, there are only 2 "curves" on your screen, but there are also two points of intersection. You will need to tell the calculator which point of intersection you want it to find by using the arrow keys to move the cursor near a point of intersection. Once you have placed the cursor near a point of intersection you can press three times to find the point.
In order to find the other point, you must perform the process again. Press and choose option 5. Move the cursor near the other point of intersection and press three times.
The process gets more complicated when you have more than a Y1 and Y2 on your graph. In other words, when you have three or more curves on your screen, it becomes important to indicate the first and second curves when the calculator prompts you. If you need to solve a problem that involves three separate graphs, consult your calculator manual for additional instructions.
you see the CALCULATE menu shown below.
and choosing option 5, you will see the screen below.
, there will be a prompt for the second curve.
again, the calculator wants a guess.
one more time to see the answer.
and choose option 5, the calculator will again prompt you for a first and second curve. As in the last example, there are only 2 "curves" on your screen, but there are also two points of intersection. You will need to tell the calculator which point of intersection you want it to find by using the arrow keys to move the cursor near a point of intersection. Once you have placed the cursor near a point of intersection you can press 
three times to find the point.
and choose option 5. Move the cursor near the other point of intersection and press 
three times.
