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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how you can solve a system of equations by graphing. Learn when you have a solution and when you don't. Also learn how easy the solution is to spot.

When it comes to math, you won't always have the luxury of solving single equations. You might just also have to solve a **system of equations**. These are problems that include more than one equation. You can have two equations, three equations, or more. To solve these types of problems, you need to take into consideration all of the equations together. Your solution needs to fit them all. There are several methods that you can use to solve a system of equations.

In this lesson, you'll learn the **graphing method**. This method involves graphing the equations to solve. It is a visual way to solve your problem. Once you have graphed your equations, all you have to do is to look at the graph to find your solution. It is very easy to spot, as you will see.

Let's take a look at how you can solve a problem such as this:

*y = 3x - 1 *

*y = 2x*

In order to use the graphing method, your equations must be in slope-intercept form so that you can easily graph them. Recall that the slope-intercept form is *y* = *mx* + *b*, where *m* is your slope and *b* is your *y*-intercept. The *y*-intercept tells you where the line crosses the *y*-axis and the *m* tells you what your slope is. After graphing the *y*-intercept, you use the slope to determine the angle of the line.

Looking at your equations, you see that they are already in slope-intercept form. If they weren't, then you would need to manipulate the equations to turn them into slope-intercept form. Since the equations are ready to use, you go ahead and graph the first line, *y* = 3*x* - 1. The *y*-intercept is -1 so you plot a point at (0, -1). Now, the slope is 3, so to find your next point from the *y*-intercept, you go up three and to the right one. This takes you to the point (1, 2). Now you connect these two dots and draw your line. You extend the line through your graph. You are done graphing the first line now.

To find your solution, you go on to graph the rest of your equations. You have just one more equation, so you go on to graph that one. The *y*-intercept is 0, so you plot a point at (0, 0). The slope is 2, so your next point is located two spaces up and one space to the right of the *y*-intercept. This next point is (1, 2). You connect these two dots and draw out your line.

Your solution can be easily spotted as the intersection of your lines. You only have two lines, so your solution is the point where these two lines meet. Do you see where your two lines meet or intersect? Yes, they intersect at the point (1, 2). This is your solution. You can give (1, 2) as your answer or you can say that your answer is *x* = 1 and *y* = 2.

All of your equations must intersect at the same point for your problem to have a solution. If your lines do not intersect, then you have a problem that is not solvable and does not have a solution. Parallel lines, for example, never intersect and, therefore, will not have a solution.

Let's look at another example:

*y = 3x - 1 *

*y - 3x = -4*

Looking at your two equations, you see that the second equation needs to be changed to the slope-intercept form. You go ahead and change it to that form by adding the 3*x* to both sides. You get this:

*y - 3x + 3x = -4 + 3x *

*y = 3x - 4*

Now your two equations are *y* = 3*x* - 1 and *y* = 3*x* - 4. You go ahead and graph these two lines on your graph. You get this:

How interesting. Your two lines don't intersect. What does this mean? It means your lines are parallel and your problem has no solution. It is not solvable. Your answer, then, is no solution.

Let's review what you've learned.

**System of equations** are problems that include more than one equation. In this video lesson, you learned about the **graphing method** of solving. This method involves graphing the equations to solve. This method involves graphing your equations and then finding the intersection of your lines. Your solution is the intersection of all your equations. Your equations need to be in the slope-intercept form so that you can easily graph them. If your lines do not intersect, then you have a problem that is not solvable and has no solution.

Use this lesson to strengthen your ability to solve a system of equations by graphing them and identifying their intersection points, if any.

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- What is a System of Equations? 8:39
- How Do I Use a System of Equations? 9:47
- How to Solve a System of Equations by Graphing 4:57
- How to Solve a System of Equations by Elimination 8:26
- How to Solve a System of Linear Equations in Two Variables 4:43
- How to Solve a Linear System in Three Variables With a Solution 5:01
- How to Solve a Linear System in Three Variables With No or Infinite Solutions 6:04
- Go to 6th-8th Grade Algebra: Systems of Linear Equations

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