top

Chapter 12—Graphing

12-5 Solving Systems of Linear Equations

Some very interesting things happen when you plot two different  linear equations on the same coordinate plane. The main thing is this:  As long as the two lines do not have the same slope, they intersect (or cross) at some point.

[show one line, two lines and point of intersection]

[if lines have the same slope, they will not  cross because they are parallel]

Graphically solve this system of linear equations
y = 2x + 1
y = -x + 4

Determine the x- and y-intercepts for the first equation and sketch line L1:

when x = 0 y = 1
when y = 0, x = - 1/2
Plot those two intercepts-- (0,1) and (0, -1/2)
Draw the straight line, L1, through those two points

Determine the x- and y-intercepts for the second equation and sketch line L2:

when x = 0,  y = 4
when y = 0, x = 4
Plot those two intercepts-- (0,4) and (4, 0)
Draw the straight line, L2, through those two points
 

The solution for the system of linear equations is the point where the two lines intersect: (1,4)

y = 2x + 1 and y = -x + 4 only when x = 1 and y = 4
   
   
   
   
   
   
   
   
   

Examples & Exercises

Given the slope and one point on a line, write the linear equation for the line in slope-intercept form.

 

 

 

 

David L. Heiserman, Editor

Copyright   SweetHaven Publishing Services
All Rights Reserved

Revised: June 06, 2015