Lesson 8 1 solving systems of linear equations by graphing answer key

Instructor: Betsy Chesnutt Show bio

Betsy has a Ph.D. in biomedical engineering from the University of Memphis, M.S. from the University of Virginia, and B.S. from Mississippi State University. She has over 10 years of experience developing STEM curriculum and teaching physics, engineering, and biology.

Linear equations form a straight line when graphed because of the constant slope. Learn how to solve linear equations by graphing them in practice problems. Updated: 11/12/2021

In this lesson, you will learn how to solve a system of linear equations by graphing. Before you can do that, though, you need to know how to recognize a system of linear equations. First, a linear equation is one that forms a line when graphed. It has two variables, usually x and y, and typically looks like this:

y = 3x + 5

or maybe this:

6y + 3x = 9

A system of linear equations is a system made up of two linear equations. To solve the system of equations, you need to find the exact values of x and y that will solve both equations. One good way to do this is to graph each line and see where they intersect.

Before you can graph a linear equation, you need to make sure that it is written in slope-intercept form:

The slope-intercept form of a linear equation is: y = mx + b.

In slope-intercept form, m is the slope of the line and b is the y-intercept, so in the equation we looked at earlier, y = 3x + 5, the slope would be 3 and the y-intercept would be 5.

• Video
• Quiz
• Course

Graphing a Linear Equation Line

Now that we know how to recognize a linear equation, let's review how to graph a line. First, you want to rearrange the equation so it's in slope-intercept form. Let's see how to do that with this equation:

3y + 9x = 18

First subtract 9x from both sides:

3y = -9x + 18

Then divide both sides by 3:

y = -3x + 6

Now, you can tell that the slope of the line (m) is -3 and the y intercept (b) is 6. To graph this line, you can use a graphing calculator or computer, but you can also do it by hand on paper. First, the y-intercept is the point where the line crosses the y axis, so you can plot this point first. Then, look at the slope. The slope is a ratio of how far the line goes up in the y direction divided by how far it goes over in the x direction.

slope = change in y / change in x

So, a slope of -3 means that you should go down 3 units in the y direction for every 1 unit you go over in the x direction. You can use that to plot a second point and then use a ruler to connect the points and make a straight line.

Solving Systems of Linear Equations

To solve a system of linear equations by graphing, you will graph both lines and then see where they intersect each other. The x and y coordinates of the intersection will be the solution to the system of equations!

Why is this intersection point the solution to the system of equations? This is the only point that falls on both lines, so it's the only combination of x and y values that will make each equation true.

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.

Become a Member

Already a member? Log In

 Back

Resources created by teachers for teachers

Over 30,000 video lessons & teaching resources‐all in one place.

Video lessons

Quizzes & Worksheets

Classroom Integration

Lesson Plans

I would definitely recommend Study.com to my colleagues. It’s like a teacher waved a magic wand and did the work for me. I feel like it’s a lifeline.

Back

Create an account to start this course today

Used by over 30 million students worldwide

Create an account