System of Equation Substitution Problem

[BookLuvr]

For a math project, my teacher wants the class to make a word problem for a system of equations that is solved by either substitution or elimination. I chose substitution. She also wants us to graph the problem. I've figured everything out for my word problem except for the graph. Nothing I try works. Here's what I've got so far:

Ken, a Salvation Army bell ringer, has quarters and nickels in his kettle. If Ken has $10.90 total and 106 coins, how many nickels and quarters does he have?

Systems:
n+q=106 (n=-q+106)
.25q+.05n=10.90

Work:
.25q+.05(-q+106)=10.90
.25q-.05q+5.3=10.90
-5.3 -5.3
.20q=5.6
_______
.20 .20
q=28
n=-28+106
n=78

How am I supposed to graph a substitution system of equations? I've looked all over the Internet and tried multiple graphing websites, but to no avail. Please help!

 

[MarkFL]

Here is the plot I obtained at www.wolframalpha.com:

 

[JeffM]

The method of finding a solution by graphing is its own method of solving a system of simultaneous equations in two unknowns. There is no way to graph substitutions; substitution and graphing are different methods to get the same answer. As Mark showed you, the graphical method is to draw the graph of each individual equation and find their intersection.

Substitution is the most general method for solving systems of simultaneous equations. Think about drawing a system of five equations in five unknowns: difficult to say the least. But it is a very simple method for solving a system of two linear equations in two unknowns.

PS Nice example problem by the way.

 

[BookLuvr]

Thank You

Thank you both! You may very well have saved my math grade! I was worried that I would have to turn the project in incomplete tomorrow.
Jeff, I agree with you. I was fairly certain that there was no possible way to graph a substitution system of equations as I could find no example of how to in my textbook or anywhere online. It might have been easier if my teacher had explained clearer on how to graph the systems in her instructions.
Once again, I cannot express how grateful I am to each of you.

 

[HallsofIvy]

For a math project, my teacher wants the class to make a word problem for a system of equations that is solved by either substitution or elimination. I chose substitution. She also wants us to graph the problem. I've figured everything out for my word problem except for the graph. Nothing I try works. Here's what I've got so far:

Ken, a Salvation Army bell ringer, has quarters and nickels in his kettle. If Ken has $10.90 total and 106 coins, how many nickels and quarters does he have?

Systems:
n+q=106 (n=-q+106)
.25q+.05n=10.90

Since these are "linear" (their graphs are straight lines and a line is determined by 2 points) it is easy graph them without a computer or calculator graphing system.

If n= 0 the first equation becomes q= 106 so the point (n, q)= (0, 106) is on its graph. If q= 0, it becomes n= 106 so (106, 0) is also on that line. Draw the straight line through the two points (0, 106) and (106, 0).

If n= 0 the second equation becomes .25q= (1/4)q= 10.90 so q= 4(10.90)= 43.6 so (0, 43.6) is on its graph. If q= 0, it becomes .05n= (1/20)n= 10.9 so n= 20(10.90)= 218 so (218, 0) is also on that line. Draw the line through (0, 43.6) and (218, 0).

Of course, the solution to the system of equations is where those two lines intersect.

Work:
.25q+.05(-q+106)=10.90
.25q-.05q+5.3=10.90
-5.3 -5.3
.20q=5.6
_______
.20 .20
q=28
n=-28+106
n=78

How am I supposed to graph a substitution system of equations? I've looked all over the Internet and tried multiple graphing websites, but to no avail. Please help!