Systems of Equations

Algebra 2 Tutorial

Systems of Equations

Intro

When solving a system of equations involving two or more variables, one must rewrite equations so that one variable is solved in terms of the other. Then the last equation can be used to “plug in” values and solve.

Sample Problem

Bob’s car dealership has 42 cars on their lot. All 42 are either sedans or SUVs. The number of SUVs is 6 less than twice the number of sedans. How many of each type are there?

Solution

Let d = number of sedans
Let v = number of SUVs

v + d = 42
v = 2d – 6

In this case the SUV today is already written in terms of the sedan total. We plug this in to the first equation:
2d – 6 + d = 42
3d – 6 = 42
3d = 48
d = 16

Use either equation to solve for v:
v = 2d – 6
v = 2*16 – 6
v = 32 – 6
v = 26

Check by adding these:

26 + 16 = 42
42 = 42

This verifies the first condition.

26 = 2*16 – 6
26 = 32 – 6
26 = 26

Both conditions are true. The solution works.



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