# Using the Calculator - Problem 2

Solving a system of equations using your calculator. So there's actually two different ways of solving a system using your calculator. The first way is the way that I typically recommend is to basically plug in so we can do our substitution like we would when we're doing algebraically. So in this case we're looking at these two equations, I would just say that we have the equation 2x plus 1 is equal to x² minus 3x minus 4. I would pull everything around to one side, so we get 0 is equal to -5x, sorry I forgot my x², 0 is equal to x² minus 5x minus 5.

I would then plug this into my calculator to look for the 0s. So I would make one equation out of it and look for the 0s. The other way to do is to plug it in as a system, so what we're going to do is to graph both of these equations and look for the intersection.

So to solve a system of equations graphically, what we want to do is go to the y equals button and put in both equations, so the equations we were looking at before are x quantity squared minus 3x minus 4, so we enter that equation. Then enter to get down to your other equation and then we graph 2 quantity x plus 1 and then we click graph.

So what we end up with is a parabola and a line that intersect at two points and we want to find those two intersection points. So what we can do is go to second calc and then you see this intersection option, so you can either scroll down to number 5 or just hit number 5 and the intersection option will come.

So what you see is it says first curve, so you scroll towards a point that looks like an intersection, hit enter, second curve the cursor is going to remain pretty close to the same spot, so hit enter once again, guess that's your approximation, it's really going to figure out no matter where you put that so hit enter one more time and what comes up is the x and the y value for this intersection, in this case we have -.8 for our x value and -.7 for our y.

What we're really concerned with is our x values. We have the y equals so we're looking for the x values here take that and then you can also see we have another point we're concerned with over on the right side. We can just scroll our cursor over to that point, do second calc intersec one more time and we can find our other intersection point.

So to solve a system of equations by using your calculator, you plug each equation in to y1 and y2, graph them a then use the second calc intersection function on your calculator to solve for the intersection points.

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