Form the pair of linear equations for the following problems and find

1.	Form the pair of linear equations for the following problems and find their solution by substitution method : The difference between two numbers is 26 and one number is three times the other. Find them.
Answer» Let one number be ‘x’. another number be ‘y’. Their difference is 26. ∴ x – y = 26 ………. (i) One number is three times the other, ∴ x = 3y …………. (ii) Substituting x = 3y in eqn. (i), x – y = 26 3y – y = 26 2y = 26 ∴ y = \( \frac{26}{2}\) ∴ y = 13 Substituting the value of ‘y’ in eqn. (ii), x = 3y ∴ x = 3 × 13 ∴ x = 39, y = 13

Form the pair of linear equations for the following problems and find their solution by substitution method : The difference between two numbers is 26 and one number is three times the other. Find them.

Answer»

Let one number be ‘x’.

another number be ‘y’.

Their difference is 26.

∴ x – y = 26 ………. (i)

One number is three times the other,

∴ x = 3y …………. (ii)

Substituting x = 3y in eqn.

(i), x – y = 26

3y – y = 26

2y = 26

∴ y = \( \frac{26}{2}\)

∴ y = 13

Substituting the value of ‘y’ in eqn. (ii),

x = 3y

∴ x = 3 × 13

∴ x = 39, y = 13