Maths

You know that p = 1 x and q = 1 y ✁
64 MATHEMATICS
These equations are not in the form ax + by + c = 0. However, if we substitute
1 1
p and
x y
q
in Equations (1) and (2), we get
2p + 3q = 13 (3)
5p – 4q = – 2 (4)
So, we have expressed the equations as a pair of linear equations. Now, you can use
any method to solve these equations, and get p = 2, q = 3.
Substitute the values of p and q to get
1 1 1 1
2, i.e., x and 3, i.e., y
x
2 y
3
.
1 1
Verification : By substituting x and ✂ ✂ y in the given equations, we find that
2 3
both the equations are satisfied.
Example 18 : Solve the following pair of equations by reducing them to a pair of
linear equations :
5 1
=2
✄
x☎
☎ 1 y 2
6 3
=1 ✆
x 1 y 2
✆
✆
Solution : Let us put
1 1
p and ✝
✝ q
x 1 y 2
. Then the given equations
1 ✞ ✟ 1
5 ✠ ✡ ☛
x 1 y 2
= 2 (1)
☎
☎
1 ✎ ✏ ✎ ✏ 1
6 ✑ ✒ ✓ ✒ ✓ 3
✕ ✔ ✕ x 1 y
✔ 2
= 1 (2)
✌
☞
✍
☞
can be written as : 5p + q = 2 (3)
6p – 3q = 1 (4)
✑
✑