Topic 5: Analyzing and Solving Systems of Linear Equations

Topic 5

Analyzing and Solving Systems of Linear Equations

By Emerson McMullen, Sage Leary, and Rune Perras

Topic 5, Lesson 1

Definitions:

-System of Equations: a set of 2 or more equations that contain 2 or more of the same
variables. For Math 8, we only used at most 2 unknown variables.

Explanation: In this lesson, you can determine the number of solutions to systems of linear
equations by analyzing graphs and comparing slopes and y-intercepts. You examine the
graphs of a linear system of equations and compare the equations in the system to
determine the number of solutions of the system. If the slopes and y-intercepts are different,
the lines intersect at 1 point, and have one solution. If the slopes are the same and the
y-intercepts are different, the lines are parallel and have no solution. If the slopes and
y-intercepts are the same, the lines are the same, therefore causing infinitely many solutions.

Emerson McMullen

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Topic 5, Lesson 1 Example

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Emerson McMullen

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Topic 5, Lesson 2

Definitions:

-One solution: The lines in which are graphed intersect at exactly one point and have only one
ordered pair that satisfies both equations.

-No solution: The lines in which are graphed do not intersect at all and are parallel.

-Infinitely Many Solutions: The lines in which are graphed intersect along every single point in
the line, as they are the same exact line.

Explanation: In this lesson, you use a graph to determine the number of solutions to a system of
linear equations. You use graphs to compare equations and solve problems. The solution of a
system of equations is a set of ordered pairs that make all of the equations in a system true. Since
the graph of a functional equation represents all ordered pairs that are solutions to the equation, if
a point lies on the graph of both functions, the point of intersection is the solution.

Sage Leary

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Topic 5, Lesson 2 Examples

Sage Leary

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Topic 5, Lesson 2 Examples Continued

Sage Leary

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Topic 5, Lesson 3

Definitions:

-“Tom Hanks”: The isolated variable.

-Substitution: The algebraic method to solve simultaneous linear equations.

Explanation: In this lesson you learn how to solve systems of equations using
substitution. You learn to isolate a variable and plug it back into the original
equation.

Rune Perras

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Topic 5, Lesson 3 Examples

Rune Perras

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