The variables x and y satisfy the equations

Question

2/x−24/y=−1
and
6/x+33/y=2.
Find the product xy.

Answer 1

2 / x − 24 / y = − 1 Divide both sides by 2

1 / x - 12 / y = - 1 / 2 Add 12 / y to both sides

1 / x - 12 / y + 12 / y = - 1 / 2 + 12 / y

1 / x = 12 / y - 1 / 2

6 / x + 33 / y = 2

6 * ( 12 / y - 1 / 2 ) + 33 / y = 2

72 / y - 6 * 1 / 2 + 33 / y = 2

72 / y - 3 + 33 / y = 2

105 / y - 3 = 2 Add 3 to both sides

105 / y - 3 + 3 = 2 + 3

105 / y = 5 Divide both sides by 5

21 / y = 1 Multipy both sides by y

y * 21 / y = 1 * y

21 = y

y = 21

1 / x = 12 / y - 1 / 2

1 / x = 12 / 21 - 1 / 2

1 / x = 3 * 4 / ( 3 * 7 ) - 1 / 2

1 / x = 4 / 7 - 1 / 2

1 / x = 8 / 14 - 7 / 14

1 / x = 1 / 14

Reciprocal:

x = 14

x * y = 14 * 21 = 294