CBSE Class 10 Maths Elimination Method

Solution

Let the number be 10x + y, x + y = 8…(1)

10x + y − (10y + x) = 18∴ x − y = 2…(2)

Adding (1) and (2),∴ 2x = 10∴ x = 5∴ y = 3∴ The number is 53.

Solution

Let the fraction be x:y.

According to the question,∴ y = 2x + 4∴ 2x − y = −4…(1)

According to the question, y − 6 = 12(x − 6)12x − y = 66…(2)Subtracting (2) from (1),

x = 7

Solution

Let the present age of the mother and daughter be x and y, respectively.

From given, x:y = 8:3∴ 3x = 8y After 5 years,∴ 4(x + 5) = 9(y + 5)∴ 4x − 9y = 25…(1)∴ 3x − 8y = 0…(2)

(1) × 3 − (2) × 4∴ 12x − 27y = 75∴ 12x − 32y = 0∴ 5y = 75∴ y = 15