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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?ANSWERThe 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.
The y-intercept is the point where a line crosses the y-axis.
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.
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.
All points represent solutions to the linear equation.
After Video
What is a system of equations?ANSWERA system of equations is a set of equations that share all the same variables.
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.
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.
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.
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
An equation that, when graphed, is a straight line.
- Solution to an equation DEFINE
A set of values for the variables in the equation that result in a true numeric equation.
- System of equations DEFINE
Two or more equations with the same variables.
- Solution to a system of equations DEFINE
A set of values for the variables in the equations that result in a true numeric equation for all equations in the system.
- Substitution method to solve systems of equations DEFINE
A method for solving systems of equations where one equation is rearranged and substituted into the other equation.
- Graphing method to solve systems of equations DEFINE
A method for solving systems of equations where both equations are graphed on a coordinate plane and the intersection is estimated visually.
- Point of intersection DEFINE
The point where two graphs intersect one another, and the solution to a system of equations
- Linear Equation DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide