Two pairs of socks and one pair of slippers cost $30. Five pairs of socks and one pair of slippers cost $42.

Question

Let x represent the cost of a pair of socks. Let y represent the cost of a pair of slippers.

this is solving systems using the elimination method 

Answer 1

2x+y=30 (2 pairs of socks + one pair of slippers = $30)

5x+y=42 (5 pairs of socks + one pair of slippers = $42)

Elimination method is basically "canceling" or subtracting so that one of the variables disappear.

If you multiply the second line of equation, 5x+y=42, by -1, the second equation becomes:

-5x-y=-42

so the new equations are:

2x+y=30

-5x-y=-42

Now you can just add them:

2x+(-5x) + y+(-y) = 30+(-42)

-3x=-12

x=4

x is the cost of one pair of socks.

now we know x, let's solve for y.

plug in 4 for x for the first equation, we get:

2(4)+y=30

8+y=30

y=22

y is the cost of one pair of slippers.

Answer 2

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 √