Graphing Systems of Equations

Date: 06/01/98 at 16:01:53
From: Kelly Sifferman
Subject: How to graph system equations

Solve the following system of equations by graphing:

    3x + 2y = 5
   -3x - 2y = 10

Thanks.

Date: 06/01/98 at 16:37:08
From: Doctor Gary
Subject: Re: How to graph system equations

Do you know how to graph a linear relation between x and y? You can 
always start with a value for x and then determine the value of y 
required to satisfy the equation. 

For example, use the equation:

   3x + 2y  =  5

If x is 0, then y must be 5/2. If x is 1, then y must be 1. Since two 
points define a line, all you have to do is draw the line that 
"connects" (0,5/2) to (1,1).

The solution to a system of linear equations is the values of x and y 
at the point at which the lines intersect.

Don't be upset that you can't solve this system, because there is no 
solution: if you multiply both sides of the second equation by -1, 
you'll see that there is no solution for this system of equations. 
3x + 2y can't be 5 and -10 at the same time.

If you graph these two lines, you'll see that they are parallel.

You can see this without graphing, by re-expressing each equation 
in the "standard" form of a linear function in which y is equal to 
the sum of (slope of the line times x) plus (y co-ordinate of the 
y-intercept). Your two equations are:

    3x + 2y  =  5
         2y  =  -3x + 5
          y  =  (-3/2)x + (5/2)

and

   -3x - 2y  =  10
        -2y  =  3x + 10
          y  =  (-3/2)x - 5

The two lines have the same slope, but they have different 
y-intercepts.

-Doctor Gary,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/