(Q1). Solve the following pair of equations

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

Observe the given pair of equations. They are not linear equations. (Why?)

We have 2(
1
x
 ) + 3(
1
y
 ) = 13 ..............(1)
5(
1
x
 ) - 4(
1
y
 ) = -2 ..............(2)
If we substitute
1
x
 = and
1
y
 = , we get the following pair of linear equations:

p + q = .................(3)

p - q = - .................(4)

Coefficients of q are 3 and 4 and their LCM is . Using the elimination method:

Equation (3) × ⇒ p + q =
Equation (4) × ⇒ p - q = - 'q' terms have opposite sign, so we add the two equations.
p =
p =
=

Substitute the value of p = in equation (3)

2() +3q = 13

3q = 13 - =

q =
3
 =
But,
1
x
 = p = ⇒ x =
1
1
y
 = q = ⇒ y =
1