Question

For what value of ‘m’ , the pair of equations x+2y-3=0 and 2x+my-7=0 has unique

solution.​

Answer 1

Step-by-step explanation:

x+2y-3 = 0 .......... eq.(1)

2x+my-7 = 0 ..........eq.(2)

from equation 1 :-

x + 2y = 3

x = 3-2y

put value of x in equation 2 :-

2x+my-7 = 0

2(3-2y)+my-7 = 0

6-4y + my - 7 = 0

(m-4)y = 1

eq(1) and eq(2) :

a1= 1

a2 = 2

b1 = 2

b2 = m

c1 = -3

c2 = -7

then

a1/a2 = b1/b2 = c1/c2

1/2 = 2/m = 3/7

m = 4

if the given system has no solution then m = 4

but in the question system of equations will have unique solution provided the lines are intersecting .

then m not equal to 4.

Answer 2

Answer:

Step-by-step explanation:

x+2y-3 = 0 .......... eq.(1)

2x+my-7 = 0 ..........eq.(2)

from equation 1 :-

x + 2y = 3

x = 3-2y

put value of x in equation 2 :-

2x+my-7 = 0

2(3-2y)+my-7 = 0

6-4y + my - 7 = 0

(m-4)y = 1

eq(1) and eq(2) :

a1= 1

a2 = 2

b1 = 2

b2 = m

c1 = -3

c2 = -7

then

a1/a2 = b1/b2 = c1/c2

1/2 = 2/m = 3/7

m = 4

if the given system has no solution then m = 4

but in the question system of equations will have unique solution provided the lines are intersecting .

then m not equal to 4.