(Q9).Solve each of the following pairs of equations by reducing them to a pair of linear equations.

2
x
 +
3
y
 = 13
5
x
 -
4
y
 = -2

where x ≠ 0, y ≠ 0

Given

2
x
 +
3
y
 = 13 and
5
x
 -
4
y
 = -2
Take
1
x
 = and
1
y
 = , then

the given equations reduce to

a + b = 13 ……… (1)

a – b = -2 ……… (2)

equation (1) × ⇒ a + b =
equation (2) × ⇒ a - b   = -
b =
⇒ b =
=

Substituting b = in equation (1) we get

2a + 3 () = 13

⇒ 2a = 13 –

⇒ a =
2
 =
but a =
1
x
 = ⇒ x =
1
b =
1
y
 = ⇒ y =
1
∴ Solution (x, y) = (
1
,
1
 )