Solving Systems of Equations by Graphing: The Best Method

Here’s How to Solve Systems of Equations by Graphing

A Short Guide for answering any Graphing Systems of Equations Example

So what exactly does it mean to know how to graph systems of equations? Solving Systems of Equations by Graphing is a way to simplify a set of two mathematical statements. The first thing you should do when Solving Systems of Equations by Graphing is to graph both mathematical statements. The easiest way to graph the equations is in Slope Intercept Form because it gives you the y-intercept and the slope. The last part when Solving Systems of Equations by Graphing is to find where the lines cross on the graph since that is your solution.

 

Solving Systems by Graphing Practice Problems Quiz

Watch the video Explanation our Systems of Equations Graphing Worksheet

Watch our free video on how to solve Systems of Equations by Graphing. This video shows how to solve problems that are on our free Graphing Systems of Equations worksheet that you can get by submitting your email above.

Watch the free Solving Systems of Equations Graphing video on YouTube here: How to Solve Systems of Equations by Graphing

 

Video Transcript:

This video is about solve system of equations by graphing. You can get the solving system of equations by graphing worksheet we use in this video for free by clicking on the link in the description below.

The first problem in our solving systems of equations by graphing worksheet gives us y equals 2x minus 3 and then y equals negative 3x plus 2. We’re looking for the solution of these two equations and the system that they make. What that means is we are looking for the point of intersection of the two equations and to solve by graphing. For example this isn’t the answer but for example if we had our graph here and we had one equation that went this way and the other equation that when you graphed it went like this, the solution to that equation would be the point of intersection. It’s the point that satisfies both equations, which would be the point that the two equations cross.

In order to solving system of equations by graphing you have to graph both equations and then you have to find the point of intersection on the graph and then that coordinate will be your answer. In order to find the point of intersection we have to first graph both equations these equations are written in slope-intercept form, which means you can use the slope and you can use the y-intercept to graph them.

In the case of the first one we know that slope-intercept form is y equals MX plus B, we know M is the slope because it’s always with the X and we know that B is the y-intercept. In the case of this equation M which is the slope is 2 and then B which is the y-intercept is negative 3, and we’re going to graph this equation in red. We have the y-intercept of negative 3 and the slope of 2. We will go down to negative 3 for the y-intercept, which is right here and then we will follow the slope which is 2 or the rise over the run, which is 2 over 1. You go up 2 and then over 1. We’ll start at our y-intercept and we’ll go up 2 over 1 I’ll go up 2 over one and so on.

Then we have to do the same thing for y equals negative 3x plus two. We have to find the slope and the y-intercept and then graph it. In this case the slope is negative 3 and then the y-intercept is positive 2. We’re going to start our y-intercept which is 2. We go up to 2 and then we’re going to graph with our slope which is negative 3. Negative 3 over 1 or down 3 and then over 1. We’ll start at our point we’ll go down 1 2 3 over 1 down 1 2 3 over 1 and we’ll graph then once we have a couple points we can go ahead and connect them. This is our second equation which is in blue.

Now the solution to our system here is going to be the point of intersection, which is right here. It’s the only point that would be true for both equations or that would satisfy the system. This point here is X is 1 Y is negative 1. Our solution to the system of equations is x equals 1 and y equals negative 1. And then in coordinates it would be 1 negative 1 and that’s the solution.

Number three on the solving systems by graphing worksheet gives us our system which in this case is y equals 4x plus 3 and the second equation is y equals negative x minus 2. For this problem of systems of equations with graphing, we have to do the same thing we did in the other problem. We’re going to go ahead and we’re going to find the slope and the y-intercept for each equation. The slope for y equals 4x plus 3 is 4 and then the y-intercept is positive 3 and then for the second equation we have y equals negative x minus 2. Our slope is even though it’s negative x what that’s like saying is that it’s actually like saying negative 1x. It’s not written but there is a one right there. That’s really negative 1x and then our y-intercept is negative two.

We’re going to go ahead and graph these. I’m gonna graph the first one in red. Our y-intercept for the first one is 3. We will go to our y axis and we’ll plot 3 and then the slope is 4. We will go up 4 and then over 1. We’ll go up 1 2 3 4 over 1 4 over 1 would be right here you could also go backwards so we’ll go down 1 2 3 4 and then this way. You can go in the negative direction and then you can go ahead and graph that equation or draw our line.

I should say then we’re gonna do the same thing for the blue equation which is y equals negative x minus 2. We’ll start at negative 2 which is right here our slope is negative 1x. We will go down 1 this time and then over 1. We’re going to go down 1 over 1 down 1 over 1 which goes in this direction and then you can always go backwards. You go up and left instead of down and right we’ll go this way. And then once we have our points plotted we can go ahead and draw our line.

And then once again in order to solve systems of equations by graphing you have to find the point of intersection between the equations. Our point of intersection is right there. It’s the spot where the two lines cross, in this case that would be negative 1 negative 1. X is negative 1 Y is negative 1. The solution X would be negative 1 Y would be negative 1 and in the terms of coordinates the solution would be negative 1 negative 1. Try all these practice problems by downloading the free solve systems by graphing worksheet above.