# Equations Reducible to a Pair of Linear Equations in Two Variables

## Notes

In the earlier concepts, we studied three methods to solve the Linear Equations, where we were directly provided with a linear equation which was in a standard form, i.e. a_1x+b_1y+c_1=0 and a_2x+b_2+c_2=0. Here, in this concept, we are required to reduce the given question into a proper linear equation and then solve it.

Example- 1/"x-1" + 2/"y-2" = 2 and 3/"x-1" - 3/"y-2" = 1

First, we need to reduce this equation in a_1x+b_1y+c=0 and a_2x+b_2y+c_2=0

For that, let's take 1/"x-1" = m and 1/"y-2" =n

So the equation becomes like, m+2n=2 ....eq1
and 3m-3n=1 ....eq2
By solving further, we get m=2-2n, substituting this in eq2
3(2-2n)-3n=1
6-6n-3n=1
-9n= 1-6

n= (-5)/-9  i.e. 5/9

Substitute n=5/9 into eq1

m+2(5/9)=2

m+ 10/9= 2

m= 2-10/9

m= 8/9

Now we will resubstitute the values of m and n in the original equations.

1/"x-1"= 8/9

8x-8= 9
8x=17

x=17/8

And 1/"y-2"= 5/9

5y-10= 9
5y= 9+10

y= 19/5

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Pair of Linear Equation in two variable part 17 (Equation reducible to linear form) [00:14:35]
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