# Solve the following pair of equations by reducing them to a pair of linear equations:

5 / (x -1) + 1 / (y - 2) = 2

6 / (x - 1) - 3 / (y - 2) = 1

**Solution:**

The standard form of a linear equation is ax + by + c = 0.

To reduce a pair of equations to the standard form, we will use substitution.

The equation 5/(x - 1) + 1/(y - 2) = 2 can be expressed 5(1 /x - 1) + 1(1/ y - 2) = 2 be equation(1)

The equation 6/(x - 1) - 3/(y - 2) = 1 can be expressed 6(1/x - 1) - 3(1/ y - 2) = 1 be equation (2)

Let 1/(x - 1) be a and 1/(y -2) be b.

⇒ 5a + b = 2 be equation (3)

⇒ 6a - 3b = 1 be equation (4).

Let us use the elimination method to find the values of a and b.

Multiply equation (3) by 3 and equation (4) by 1.

⇒ 15a + 3b = 6 be equation (5)

Add equation (4) and (5)

⇒ (15a + 3b = 6) + (6a - 3b = 1)

⇒ 21a = 7

⇒ a = ⅓

Substitute a = ⅓ in equation (3)

5(⅓) + b = 2

5 + 3b = 6

b = ⅓

∵ a = ⅓ ; b = ⅓

the value of x - 1 = 3; y - 2 = 3.

∴ x = 4; y = 5

☛ Check: NCERT Solutions for Class 10 Maths Chapter 3

## Solve the following pair of equations by reducing them to a pair of linear equations: 5 / (x -1) + 1 / (y - 2) = 2, 6 / (x - 1) - 3 / (y - 2) = 1

**Summary:**

The values of x and y for the pair of linear equations is 4 and 5 which satisfies the equation

**☛ Related Questions:**

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