# Applications of Linear Systems

This video shows how linear systems can be applied in word problems.

When you encounter a word problem, it is important to write down all the important information given to you.
You would then use that information to write out the equations needed to solve the problem.
In this case, its substitution by elimination, where you solve for one variable by eliminating the other variable, and then plugging your answer back into an original equation to find the other variable.
Be sure to write in the units used by the word problems.

Example:

Li and Jordan went to the store. Li bought 3 boxes of cereal and 5 muffins for \$22. Jordan bought one box of cereal and eight muffins for \$20.
What is the cost of a box of cereal?
What is the cost of a muffin?

$3c + 5m = 22$
$\underline{-3( c + 8m = 20 )}$

$3c + 5m = 22$
$\underline{-3c - 24m = -60}$
$-19m = -38$
$m = 2$
$\downarrow$
$c + 8m = 20$
$c + 8(2) = 20$
$c + 16 = 20$
$c = 4$

Cost of a box of cereal = \$4
Cost of a muffin = \$2

• ## Want full access to all of our free math tutorials & practice problems?

Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II