sorry brother I can't give answer of this question

I try to this but I can't get right answer

Verified answer

Answer:

search-icon-header

Search for questions & chapters

search-icon-image

Question

Bookmark

Determine the values of m and n so that the following system of linear equations have infinite number of solutions:

(2m−1)x+3y−5=0

3x+(n−1)y−2=0

Medium

Solution

verified

Verified by Toppr

This system of equation is of the form

a

1

x+b

1

y+c

1

=0

a

2

x+b

2

y+c

2

=0

where a

1

=2m−1,b

1

=3,c

1

=−5

and a

2

=3,b

2

=n−1 and c

2

=−2

For infinitely many solutions, we must have

a

2

a

1

=

b

2

b

1

=

c

2

c

1

The given system of equations will have infinite number of solutions, if

3

2m−1

=

n−1

3

=

−2

−5

⇒

3

2m−1

=

n−1

3

=

2

5

⇒

3

2m−1

=

2

5

and

n−1

3

=

2

5

⇒4m−2=15 and 6=5n−5

⇒4m=17 and 5n=11

⇒m=

4

17

and n=

5

11

Hence, the given system of equations will have infinite number of solutions, if m=

4

17

and n=

5

11

.