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 represent the constraints in the situation.
x + y = 4.25
16.90x + 4y = 36.35
1. What does the solution to the system represent?
2. Find the solution to the system of equations. Explain or show your reasoning.
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Silk = x = 1.5 yards

Cotton = y = 2.75 yards

Step-by-step explanation:

x + y = 4.25

16.90x + 4y = 36.35

1. The solution to the equation represent number of yards of silk and number of yards of cotton bought.

2.

x + y = 4.25 (1)

16.90x + 4y = 36.35 (2)

Multiply (1) by 4

4x + 4y = 17 (3)

16.90x + 4y = 36.35 (2)

Subtract (3) from (2)

16.90x - 4x = 36.35 - 17

12.90x = 19.35

Divide both sides by 12.90

x = 19.35 / 12.90

= 1.5

x = 1.5 yards

Substitute x = 1.5 yards into (1)

x + y = 4.25

1.5 + y = 4.25

y = 4.25 - 1.5

= 2.75

y = 2.75 yards

Silk = x = 1.5 yards

Cotton = y = 2.75 yards

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step-by-step explanation: