# Northwestern Technical College System of Equations Worksheet

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Please fill out these system of equation assignments. Answer all questions fully and add units if needed

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System of Equations
Name___________________________________
1. Remember the tuition problem where you paid \$200 per credit plus fees of \$350.
a.
Consider the linear equation that gives the amount spent in terms of the number of credits
taken.
What should the independent variable represent?
What should the dependent variable represent?
Write the linear equation that gives the amount spent in terms of the number of credits taken.
What is the slope? Write a sentence interpreting the meaning of the slope.
What is the y-intercept? Write a sentence interpreting the meaning of the y-intercept.
b. Let’s say you only have \$3200 to spend for tuition and fees. How many credits can you take?
c. Now let’s look at this graphically. Go to www.desmos.com
Be sure Equations is selected. Let y = 3200 and y = 200x + 350
d. To find where 3200 = 200x + 350 graphically: Click where the 2 graphs cross.
What do you get?
Interpret what this means?
How does this compare to the result you found algebraically?
e. How many credits can you take if you want to spend at most \$3600? How would you solve this
algebraically?
f. How would you solve part e graphically?
System of Equations – 2
Name___________________________________
1. The BSU Track Team is planning to sell t-shirts at the NSIC Conference Track Meet. Thunderbird
Graphics charges \$25 to set up a screen print with the NSIC Logo (\$25 is called a fixed cost. No matter
how many t-shirts they purchase they still need to pay \$25.) and \$5.75 a t-shirt (this cost depends on
how many t-shirts they sell, so it is a variable cost.). They plan to sell the t-shirts for \$10 a shirt.
a. Consider the linear equation that gives the amount spent in terms of the number of t-shirts
purchased.
What should the independent variable represent?
What should the dependent variable represent?
Write the linear equation that gives the amount spent in terms of the number of t-shirts purchased.
What is the slope? Write a sentence interpreting the meaning of the slope.
What is the y-intercept? Write a sentence interpreting the meaning of the y-intercept.
b. Consider the linear equation that gives the amount of money you take in for the sale of the t-shirts.
This equation is called your revenue equation.
What should the independent variable represent?
What should the dependent variable represent?
Write the linear equation that gives the amount of money you take in for the sale of the t-shirts.
What is the slope? Write a sentence interpreting the meaning of the slope.
What is the y-intercept? Write a sentence interpreting the meaning of the y-intercept.
c. The break-even point is where revenue equals cost. Find the break-even point for the NSIC t-shirt
problem. Set the revenue equation equal to the cost equation and solve for the number of t-shirts.
Revenue
=
Cost
d. Now let’s look at this graphically. Click on this address or copy this web address into your internet
browser: http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html
Be sure Equations is selected. Let y1 be revenue and y2 be cost.
Select Settings. Input appropriate values
Press: Graph
Mark on your graph above where Revenue equals Cost. You found this algebraically. To find the
break-even point graphically, Select: Intersection, Click in each box by the equations and then Press:
Find Intersection Point(s).
What do you get?
How does this compare to the break-even point you found algebraically?
e. When does revenue exceed cost? How would you find this algebraically? graphically?
f. When does cost exceed revenue? How would you find this algebraically? graphically?
g. What is the fewest number of t-shirts the Track Team needs to sell in order to make a profit?
2. Thunderbird Graphics sells different quality t-shirts. The price per t-shirt is \$4.75 for this t-shirt.
a. What would the cost equation be?
b. What is the slope? Write a sentence interpreting the slope.
c. What is the y-intercept? Write a sentence interpreting the y-intercept?
d. How many t-shirts would the Track Team have to sell to break even?
e. How does the number of t-shirts compare to the result you got when the price was \$5.75 a t-shirt?
f. What should the BSU Track Team consider as they decide which t-shirt to purchase for the
Conference Track Meet?

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system of equations

BSU Track Team

NSIC Conference

Track Meet

Thunderbird Graphics

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