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Before you get started, take this readiness quiz.
Previously in this chapter we solved several applications with systems of linear equations. In this section, we’ll look at some specific types of applications that relate two quantities. We’ll translate the words into linear equations, decide which is the most convenient method to use, and then solve them.
We will use our Problem Solving Strategy for Systems of Linear Equations.
Many of the problems we solved in earlier applications related two quantities. Here are two of the examples from the chapter on Math Models .
In that chapter we translated each situation into one equation using only one variable. Sometimes it was a bit of a challenge figuring out how to name the two quantities, wasn’t it?
Let’s see how we can translate these two problems into a system of equations with two variables. We’ll focus on Steps 1 through 4 of our Problem Solving Strategy.
Translate to a system of equations:
The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.
Translate to a system of equations:
The sum of two numbers is negative twenty-three. One number is 7 less than the other. Find the numbers.
Translate to a system of equations:
The sum of two numbers is negative eighteen. One number is 40 more than the other. Find the numbers.
We’ll do another example where we stop after we write the system of equations.
Translate to a system of equations:
A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?
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