Question

Determine the value for m and n so that the following pair of linear equations have infinite number of solutions.

2(m-1)x+3y=5, 3x+(n-1)y=2.

Answer 1

2(m-1)x+3y=5,a1=2(m-1),b1=3& c1=5
3x+(n-1)=2,a2=3,b2=n-1 &c2=2

for infinite solution,
a1/a2=b1/b2=c1/c2
Now,
a1/a2=c1/c2
2m-2/3=5/2
2m-2=15/2
m=19/4
Now,
b1/b2=c1/c2
3/n-1=5/2
6=5n-5
n=11/5

Therefore for m=19/4 and n=11/5 the pair of linear equation will have infinite solution.

Answer 2

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

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Given :- 2(m-1)x+3y=5,

             3x+(n-1)y=2.

             Pair of linear equations have infinite number of solutions.

To find :- The value for m and n .

Solution :-

2( m-1 )x + 3y - 5 = 0

3x + ( n-1 )y - 2 = 0

Given system of equations will have infinite number of solutions if,

2m-1/3 = 3/n-1 = -5/-2

2m-1/3 = 3/n-1 = 5/2

2m-1/3  =  5/2 and  3/n-1 = 5/2

4m-2 = 15 and 6 = 5n-5

4m = 17 and 5n = 11

m = 17/4 and n = 11/5

The given system of equations will have infinite number of solutions , if m= 17/4 and n = 11/5.

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