The slope is the rise over the run, or the change in y over the change in x. It describes how steep or shallow the slant of a line is on a coordinate plane.

What is the y-intercept?

The y-intercept is the point where a line crosses the y-axis.

What is a linear equation?

A linear equation is the equation of a line that increases or decreases at a constant rate. A linear equation produces a graph that is a straight line.

Jenna is driving her car. Her gas tank holds 15 gallons of gas. If she can drive 100 miles per gallon of gas, what linear equation represents how much gas is in Jenna’s gas tank?

Let x represent the distance driven, and let y represent the amount of gas in Jenna’s tank. Then the slope of the equation is –1gal/100mi and the y-intercept is 15. This means the equation is y = [ggfrac]1/100[/ggfrac]x + 15.

What is true about all points on the graph of a linear equation?

All points represent solutions to the linear equation.

What is a system of equations?

A system of equations is a set of equations that share all the same variables.

What is the substitution method?

The substitution method is a method for solving a system of equations. In this method, one equation is set equal to a single variable and then substituted into the other equation.

What is the graphing method?

The graphing method is a method for estimating the solution to a system of equations. In this method, two linear equations are graphed on the same coordinate plane. The point where the two lines intersect is the solution to the system.

Does it matter what variable you rearrange for in the substitution method?

No, I get the same answer no matter which variable I rearrange for, or which equation I rearrange first. There may be one variable that is easier to solve for first, in which case I may choose to solve that one first, but I don’t need to.

When you verify a solution to a system of equations, do you need to check the solution in all the equations in the system?

Yes; it is possible that a point is on one line and not the other. The solution to a system needs to be on both lines, so I need to check both equations.

Solve Systems of Equations

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What you will learn from this videoWhat you will learn

We will learn that when you have TWO equations that share the same variables we call that a system of equations.
We will learn to solve them by graphing OR by using algebra.
And we'll see how this knowledge can help us have a bbq, work at a roller-rink, and even take care of animals!

Discussion Questions
- Before Video
  What is slope?ANSWER
  - The slope is the rise over the run, or the change in y over the change in x. It describes how steep or shallow the slant of a line is on a coordinate plane.
  What is the y-intercept?ANSWER
  - The y-intercept is the point where a line crosses the y-axis.
  What is a linear equation?ANSWER
  - A linear equation is the equation of a line that increases or decreases at a constant rate. A linear equation produces a graph that is a straight line.
  Jenna is driving her car. Her gas tank holds 15 gallons of gas. If she can drive 100 miles per gallon of gas, what linear equation represents how much gas is in Jenna’s gas tank?ANSWER
  - Let x represent the distance driven, and let y represent the amount of gas in Jenna’s tank. Then the slope of the equation is –1gal/100mi and the y-intercept is 15. This means the equation is y = [ggfrac]1/100[/ggfrac]x + 15.
  What is true about all points on the graph of a linear equation?ANSWER
  - All points represent solutions to the linear equation.
- After Video
  What is a system of equations?ANSWER
  - A system of equations is a set of equations that share all the same variables.
  What is the substitution method?ANSWER
  - The substitution method is a method for solving a system of equations. In this method, one equation is set equal to a single variable and then substituted into the other equation.
  What is the graphing method?ANSWER
  - The graphing method is a method for estimating the solution to a system of equations. In this method, two linear equations are graphed on the same coordinate plane. The point where the two lines intersect is the solution to the system.
  Does it matter what variable you rearrange for in the substitution method?ANSWER
  - No, I get the same answer no matter which variable I rearrange for, or which equation I rearrange first. There may be one variable that is easier to solve for first, in which case I may choose to solve that one first, but I don’t need to.
  When you verify a solution to a system of equations, do you need to check the solution in all the equations in the system?ANSWER
  - Yes; it is possible that a point is on one line and not the other. The solution to a system needs to be on both lines, so I need to check both equations.
Vocabulary
- Linear Equation DEFINE
- Solution to an equation DEFINE
- System of equations DEFINE
- Solution to a system of equations DEFINE
- Substitution method to solve systems of equations DEFINE
- Graphing method to solve systems of equations DEFINE
- Point of intersection DEFINE
Reading Material
Practice Word Problems
Practice Number Problems
Lesson Plan
Teacher Guide
Assessment
Online Quiz Game Quiz PDF Exit Ticket