SIMPLE WORD PROBLEMS RESULTING IN A SYSTEM OF EQUATIONS
LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
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Many word problems, upon translation, result in two equations involving two variables (two ‘unknowns’).
In mathematics, a collection of more than one equation being studied together is called a system of equations.

The systems in this section are fairly simple, and can be solved by substituting information from one equation into the other.

The procedure is illustrated with the following example:

Antonio loves to go to the movies. He goes both at night and during the day. The cost of a matinee is \$6.00. The cost of an evening show is \$8.00. If Antonio went to see a total of $\,12\,$ movies and spent \$86.00, how many night movies did he attend?

THE GOOD NEWS!

Even though this explanation was very long, you'll actually be writing down very little!
Here's the word problem again, and what I ask my students to write down:

Antonio loves to go to the movies. He goes both at night and during the day. The cost of a matinee is \$6.00. The cost of an evening show is \$8.00. If Antonio went to see a total of $\,12\,$ movies and spent \$86.00, how many night movies did he attend?

Let $\,n = \text{# night tickets}\,$.
Let $\,d = \text{# day tickets}\,$.
$n + d = 12$
$8n + 6d = 86$
$n = 12 - d$
$8(12-d) + 6d = 86$
$96 - 8d + 6d = 86$
$96 - 2d = 86$
$-2d = -10$
$d = 5$   (circle this)
$n + 5 = 12$
$n = 7$  (circle this)
$7 + 5 \,\,\overset{\text{?}}{=}\,\,12$  
$8(7) + 6(5) \,\,\overset{\text{?}}{=}\,\,86$  

Antonio attended  7  night movies.
Master the ideas from this section
by practicing the exercise at the bottom of this page.


When you're done practicing, move on to:
Introduction to Matrices

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6 7
AVAILABLE MASTERED IN PROGRESS

(MAX is 7; there are 7 different problem types.)