Problem 66 - Algebra and Trigonometry

Question

What is the fastest method for solving a linear system with your graphing utility?

Step-by-Step Solution

Answer

The fastest method to solve a linear system using a graphing utility involves understanding the system, entering the equations into the utility, graphing them, identifying the intersection point, and then confirming this point as the solution.

Step 1: Understand the System

The first step requires you to understand the system of linear equations you want to solve. This system will be comprised of two or more linear equations.

Step 2: Enter the Equations

In this step, you'll need to enter each equation separately into your graphing utility. This is usually done through a specific input function in the software or device being used.

Step 3: Graph the Equations

Once entered, the next task is to graph the equations. This will be done by the graphing utility once the equations are entered correctly. Each equation will yield a straight line on the graph.

Step 4: Identify the Intersection

After graphing, identify the intersection of the lines if one exists. This intersection point represents the solution of the system of equations. If no intersection exists or the lines overlap, it shows that system has no solution or an infinite number of solutions respectively.

Step 5: Confirming the Solution

The last step is to confirm the solution. Recollect that the solution to a system of equations is the ordered pair (x, y) that makes all the equations in the system true. Substitute the coordinates of the intersection point as the values of x and y for each equation in the system to ensure they hold true.