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Chapter 7: Problem 67

Explain how to solve a system of equations using graphing.

Short Answer

Expert verified
The solution of a system of equations can be found by graphing each equation individually and identifying the point where the two lines intersect. This intersection point represents the \(x\) and \(y\) values that satisfy both equations simultaneously.

Step by step solution

01

Understanding a System of Equations

A system of equations is a set of two or more equations with the same variables. The solution to the system is the values that make all the equations true at the same time. The solution to a system of two linear equations can be visualised as the point where the graphs of the two equations intersect.
02

Graphing the Equations

To solve the system, each equation must be graphed individually. Start by converting the equations into slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Using the slope and y-intercept, plot each equation on a graph.
03

Finding the Point of Intersection

The solution to the system of equations is the point where the graphs intersect. This point represents the values of \(x\) and \(y\) that satisfy both equations simultaneously.
04

Verification of Solution

To ensure that the found point is indeed the solution to the system, substitute the \(x\) and \(y\) values of the point into both original equations. If the equations hold true, then the found point is the correct solution.

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Most popular questions from this chapter

Graph each linear inequality. \(x \leq 2\)

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