Question

Find whether the following pair of equations has no solution, unique solution or infinitely many solutions.

5x-8y+1 = 0 ;
3x-24/5y+3/5 = 0​

Answer 1

Step-by-step explanation:

Given System of equations are:

5x−8y+1=0

3x−

5

24

y+

5

3

=0

From equation (2) will get

15x−24y+3=0

Now from equation (1) and (2) will have:

a

2

a

1

=

15

5

,

b

2

b

1

=

−24

−8

,

c

2

c

1

=

3

1

⇒

a

2

a

1

=

3

1

,

b

2

b

1

=

3

1

,

c

2

c

1

=

3

1

Therefore, system of equations have Infinitely many solutions.

Answer 2

Given System of equations are:

5x−8y+1=0

3x−524y+53=0

From equation (2) will get

15x−24y+3=0

Now from equation (1) and (2) will have:

a2a1=155,b2b1=−24−8,c2c1=31

⇒a2a1=31,b2b1=31,c2c1=31

Therefore, system of equations have Infinitely many solutions.