# Pair of Linear Equation

**Fast trick to solve Pair of linear equation**

##### Q1. **4x + 3y = 9** and **8x + 27y = 81**

#####
where a1 = 4 and
a2 = 8

b1 = 3 and
b2 = 27

c1 = 9 and
c2 = 81

Now lets check whether -

^{b1}/_{b2} = ^{c1}/_{c2} or ^{b1}/_{b2} = ^{c1}/_{c2}

If any of the above condition matched only then we can use this method to solve the equation.

In the above question as we see its matched with the condition 2 so -

^{b1}/_{b2} = ^{c1}/_{c2}

^{3}/_{27} = ^{9}/_{81}

^{1}/_{9} = ^{1}/_{9}

If the condition satisfied then we take x equals to 0.

x = 0

3y = 9

y = 9/3

y = 3/1

**y = 3/1**

^{b1}/

_{b2}=

^{c1}/

_{c2}

^{b1}/

_{b2}=

^{c1}/

_{c2}

##### Q1. **2x + 3y = 7** and **4x + 8y = 14**

#####
where a1 = 2 and
a2 = 4

b1 = 3 and
b2 = 8

c1 = 7 and
c2 = 14

Now lets check whether -

^{b1}/_{b2} = ^{c1}/_{c2} or ^{b1}/_{b2} = ^{c1}/_{c2}

If any of the above condition matched only then we can use this method to solve the equation.

In the above question as we see its matched with the condition 1 so -

^{a1}/_{a2} = ^{c1}/_{c2}

^{2}/_{4} = ^{7}/_{14}

^{1}/_{2} = ^{1}/_{2}

If the condition satisfied then we take y equals to 0.

y = 0

2x = 7

y = 7/2

y = 7/2

**y = 7/2**

^{b1}/

_{b2}=

^{c1}/

_{c2}

^{b1}/

_{b2}=

^{c1}/

_{c2}