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Solving Systems of Equations by Graphing - Problem 1
To solve a system of equations by graphing, graph each equation and identify the point where the two lines intersect. That point is the solution to the system of equations -- it is where the x and y values of the two equations are equal. Check the solution by plugging the values into each equations. If the equations are true, meaning that the two sides of the equations equal each other, then the solution is correct.
This is the system of equations that I’m asked to solve by graphing. What that means is that I have to graph both lines and find where they cross. The problem now also asked me to check my solution, so once I get the point that I think is right, I’m going to substitute those values back into both equations and verify that I get equalities.
So let’s do it. First thing I’m going to do because I’m a visual person I like color, I’m going to designate that this first equation I’m going to graph in red and the second equation I’m going to graph in blue. That might be able to help me keep track which line is which. Okay so for this line I’m going to put the first dot at the y intercept at 4, from there I’ll count the slope up 1 over 1.
My first dot goes at the y intercept at 4, from there I’m going to count the slope which is up 1 over 1. I’m going to do a few different points in both directions so I can make sure my graph’s going to be precise. Again you guys, it’s absolutely critical when you’re solving systems by graphing that you’re accurate otherwise you’re going to get the wrong intersection point, the wrong answer. Okay there is my red line.
My next line is a little bit different. I’m going to want to put my first dot at the y intercept of 1, from there I’m going count the slope up 4 over 1 to the right. So here we go, starting at 1 is my first dot. From there I’m going to count up 4, right 1. 1, 2, 3, 4 right 1. 1, 2, 3, 4 right 1. 1, 2, 3, 4 right oops 1, 2, 3, 4 right 1 okay. Do a couple of points so you guys can make sure your graph’s right. Use your ruler absolutely, absolutely to draw and then find where the lines cross.
The whole point of solving a system of equations is looking for the solution. The solution is the point where the lines cross, or they intersect and intersect means cross. So let’s looks here the point where these lines cross is 1, 2, 2, 3, 4, 5; (1,5) I think that’s my answer. Let’s go over and double check using substitution to make sure that’s correct.
So first, in the red equation, I want to see if my y number is equal to my x number plus 4. So is it true that 5 equals 1 plus 4? Yeah, they’re equal good so that works in the first equation, but in order to be a solution, it has to work in both, so I’m not done checking yet. Let’s look at the blue equation. Let’s see if when I plug in my point that I think is right, I get an equality. Is it true that 5 equals 4 times 1 plus 1? Yeah sweet great this tells me that since the point is a solution to both of these original equations then I did it correctly. That’s good because I don’t like graphing and I don’t want to have to do that guy again.
Make sure you guys are precise the first time around. I’m not playing here, you’ve got to use graph paper and you have to use a ruler otherwise you’re not going to be getting these to both check out correctly.