Aaron Rafter's Absorb Assignment

Solving Systems of Linear Equations

For an introduction, click here.

To download Graph, the free graphing software, click here.

Formal Definition

A system of linear equations is a grouping of two or more linear equations, each of which contains one or more variables.

Processes and Algorithms

Solving by Substitution

Solve an equation for one of the variables and then substitute that into the other equation

Solving by Substitution

Example 1

Example 2

Solving by Elimination

Add multiples of each equation together to eliminate one of the variables

Solving by Elimination

Example 1

Example 2

Solving by Graphing Equations

Graph the two lines to see where they intersect (if they intersect).

Solving by Graphing Equations

Example 1

Critical Thinking and Application

Example 2

Critical Thinking and Application

Example 1

Example 2

Further Challenges:

Example:

A nutritionist recommends that your daily intake of Vitamin C should be 40 mg and your daily intake of Vitamin D should be 30 mg. GNC stocks two products that contain the vitamins. One compound contains 20% vitamin C and 30% vitamin D, while the other contains 40% vitamin C and 20% vitamin D. How many milligrams of each compound should you take to fulfill your daily intake recommendation?

Example:

Suppose car A travels at an average speed of 65 miles per hour while car B travels at an average speed of 50 miles per hour. In the time it takes car B to travel a certain distance, d, car A travels 75 miles farther. Find the distance traveled by each car, and the time of its trip.

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