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