(Q4).Solve each of the following pairs 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

Given

5
x - 1
 +
1
y - 2
 = 2
6
x - 1
 +
3
y - 2
 = 1
Put
1
x - 1
 = and
1
y - 2
 = ,

then the given equations reduce to

a + b = 2 ……… (1)

a – b = 1 ………. (2)

equation (1) × ⇒ a + b=
equation (2) × ⇒ a - b =
b =
⇒ b =
=
1
Substituting b =
1
 in equation (1) we get
5a +
1
 = 2 ⇒ 5a = 2 -
1
⇒ 5a =
× -
⇒ 5a =
-
⇒ a =
×
1
 =
1
but a =
1
x - 1
 ⇒
1
 =
1
x - 1

⇒ (x – 1) . 1 = × 1

⇒ x – 1 =

⇒ x = + 1 =

b =
1
y - 2
 ⇒
1
 =
1
y - 2

⇒ (y – 2) . 1 = × 1

⇒ y – 2 =

⇒ y = + 2 =

∴ Solution (x, y) = (, )