Problem 57 - Introductory Algebra for College Students

Question

Explain how to solve a system of linear equations by graphing.

Step-by-Step Solution

Answer

The system of linear equations is solved by graphing the individual equations and identifying their point, or points, of intersection, which is the solution to the system.

Step 1: Understand the Equations

First, take a quick look at your linear equations. Make sure they're in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. If they're not in this form, rearrange them. These equations will create straight lines when graphed.

Step 2: Graph the Equations

The next step is to draw each equation on a graph. Plot the y-intercept first, then use the slope to find a second point for each line. Sketch the lines extending through these points.

Step 3: Identify Intersection

Look at the graph and identify where the lines intersect each other. That point represents the x and y values that solve the system of equations.

Step 4: Write the Solution

The solution of a system of equations represented by graph is the point of intersection. Identify the x and y coordinates of the point, and write them as an ordered pair \((x, y)\). This is the solution to the system.