Question

Two pairs of socks and a pair of slippers cost $30. Five pairs of socks and a pair of slippers cost $42. Let x represent the cost of a pair of socks and let y represent the cost of a pair of slippers.

Identify the system of equations that represents the situation and identify the solution to the system of equation.

Answer 1

y=22

Explanation:

Take the second statement as equation 1 and the first statement as equation 2 and subtract to eliminate y:

5x + y = 42

-(2x + y = 30)

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3x + 0 = 12 --> x = 4

substituting x = 4 into 2x + y = 30 --> 8 + y = 30 --> y = 22

(x,y) = (4,22)

checking by adding the two equations substituting in (4,22)

20 + 22 = 42

8 + 22 = 30

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28 + 44 = 72

72 = 72 √

Answer 2

4, 22 See below

Explanation:

2x + y = 30

5x + y = 42

Subtract the first from the second

3x = 12

x = 4 so socks cost $4

Put that into one of the original equations

2x + y = 30

2(4) + y = 30

8 + y = 30

y = 22 slippers cost $22