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Exploring a System of Equations

2.1.4 Exploring a System of Equations

2.1.4 • Exploring a System of Equations

Cool Down

At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard, and cotton is $4 per yard.

Here is a system of equations that represents the constraints in the situation.

{x+y=4.2516.90x+4y=36.35{x+y=4.2516.90x+4y=36.35

1.

What does the solution to the system represent?

Compare your answer:

Your answer may vary, but here is a sample. The solution represents the combination of lengths of silk and cotton (in yards) that meet both constraints: they add up to 4.25 yards, and the cost of buying both is $36.35.

2.

Find the solution to the system of equations.

Compare your answer:

1.5 yards of silk and 2.75 yards of cotton.

3.

Explain or show how you know the solution solves the system.

Compare your answer:

Your answer may vary, but here is a sample.

  • The graphs of the equations intersect at (1.5,2.75)(1.5,2.75) Graph of two lines in the first quadrant. The y-axis is labeled cotton (yards), and the x-axis is labeled sild (yards).
  • Solving by using a table gives x=1.5x=1.5 and y=2.75y=2.75.