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.
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 [beautiful math coming... please be patient] $\,12\,$ movies and spent \$86.00, how many night movies did he attend? 
ENGLISH WORDS  TRANSLATION INTO MATH  NOTES/CONVENTIONS 
“Antonio went to see a total of 12 movies”  [beautiful math coming... please be patient] $n+d = 12$ 
NOTE: There are many realnumber choices for $\,n\,$
and $\,d\,$ that make this equation true. Here are a few:
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$0 + 12 = 12$
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$1 + 11 = 12$
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$1.3 + 10.7 = 12$
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$(2) + 14 = 12$
Of course, we want whole number solutions, and we also need something else to be true.

“... and spent \$86.00”  [beautiful math coming... please be patient] $8n + 6d = 86$  Each night movie costs \$8.00, so $\,n\,$ night movies cost $\,8n\,$ dollars. Each day movie costs \$6.00, so $\,d\,$ day movies cost $\,6d\,$ dollars. Both [beautiful math coming... please be patient] $\,8n\,$ and $\,6d\,$ have units of dollars. Also, the number $\,86\,$ has units of dollars. It's important that you have the same units on both sides of the equal sign. Here, we have: dollars plus dollars is dollars. CONVENTION: Write [beautiful math coming... please be patient] $\,8n\,$, not (say) $\,8.00n\,$ or $\,\$8n\,$ or $\,\$8.00n\,$. NOTE: Convince yourself that there are also infinitely many realnumber choices for [beautiful math coming... please be patient] $\,n\,$ and $\,d\,$ that make this equation true. We want a choice for [beautiful math coming... please be patient] $\,n\,$ and a choice for $\,d\,$ that make BOTH equations true at the same time. 
[beautiful math coming... please be patient] $8(12  d) + 6d = 86$  original equation 
[beautiful math coming... please be patient] $96  8d + 6d = 86$  distributive law 
[beautiful math coming... please be patient] $96  2d = 86$  combine like terms 
[beautiful math coming... please be patient] $2d = 10$  subtract $\,96\,$ from both sides 
[beautiful math coming... please be patient] $d = 5$  divide both sides by$\,2\,$ 
[beautiful math coming... please be patient] $n+d = 12$  the simple equation 
[beautiful math coming... please be patient] $n + 5 = 12$  substitute in the known information 
[beautiful math coming... please be patient] $n = 7$  subtract $\,5\,$ from both sides 
EQUATIONS  CHECK  TRUE? 
[beautiful math coming... please be patient] $n + d = 12$  [beautiful math coming... please be patient] $7 + 5 \,\,\overset{\text{?}}{ = }\,\, 12$  Yes! 
[beautiful math coming... please be patient] $8n + 6d = 86$  [beautiful math coming... please be patient] $8(7) + 6(5) \,\,\overset{\text{?}}{ = }\,\, 86$  Yes! (Feel free to use your calculator.) 
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
[beautiful math coming... please be patient]
$\,n = \text{# night tickets}\,$. Let [beautiful math coming... please be patient] $\,d = \text{# day tickets}\,$.
[beautiful math coming... please be patient] $8(7) + 6(5) \,\,\overset{\text{?}}{=}\,\,86$ ☺ Antonio attended 7 night movies. 
On this exercise, you will not key in your answer. However, you can check to see if your answer is correct. 
PROBLEM TYPES:
