Solve the system graphically. See Example 5. { x-3 y =-2 5 x+3 y =17.

Name: Problem 41, Chapter 5: College Algebra and Calculus: An Applied Approach
Uploaded: 2021-07-01T16:39:57-08:00
Duration: 1 min 48 s
Channel: Jennifer Stoner
Description: Solve the system graphically. See Example 5. { x-3 y =-2 5 x+3 y =17.

step 1 Given the system of equations, X minus 3Y equals negative 2 and 5x plus 3Y equals 17, we can sol

Solve the system graphically. See Example 5. { x-3 y =-2...

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Key Concepts

System of Linear Equations

A system of linear equations involves two or more linear equations that are solved together, meaning the solution must satisfy each equation in the system. The graphical approach represents each equation as a line on the coordinate plane, and the intersection of these lines indicates the set of solutions that work for all equations.

Graphical Method

The graphical method is a visual approach to solving systems of equations where each equation is plotted on the same set of axes. The point where the graphs intersect, if any, is the solution to the system, as it represents the values of the variables that satisfy all equations simultaneously.

Slope and Intercept

In order to graph a linear equation easily, the equation is often rewritten in slope-intercept form (y = mx + b). This form reveals the slope (m), which indicates the steepness and direction of the line, and the y-intercept (b), which shows where the line crosses the y-axis, making graphing straightforward.

Intersection Point

The intersection point of the graphs of the equations is the set of coordinates that satisfies every equation in the system. If the lines intersect at exactly one point, the system has a unique solution; if they overlap entirely, there are infinitely many solutions; and if they never intersect, the system has no solution.

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