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Equations Reducible to a Pair of Linear Equations in Two Variables

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  • Equations Reducible to Linear Equations

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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 of all 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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Shaalaa.com | Pair of Linear Equation in two variable part 17 (Equation reducible to linear form)

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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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