Question

3. Obtain the condition for the following system of linear equations to have a unique solution :
ax + by = c and mx + ny = 1.
4. Determine whether the pair of linear equations x – 3y = -5 and 3x + 9y = 15 has a unique
solution, no solution or infinitely many solutions.​

Answer 1

Answer:

3.Answer

ax+by=6

lx+my=n

Comparing ax+by−c=0

with a

1

x+b

1

y+c

1

=0

a

1

=a,b

1

=b,c

1

=−c

Comparing lx+my−n=0

with a

2

x+b

2

y+c

2

=0

a

2

=l,b

2

=m,c

2

=−n.

∴ For a unique solution ,

a

2

a

1



=

b

2

b

1

⇒

l

a



=

m

b

⇒am



=bl

Step-by-step explanation:

4.The given system of equations is: x − 3y – 3 = 0 3x − 9y − 2 = 0 T

he above equations are of the form a1 x + b1 y − c1 = 0 a2 x + b2 y − c2 = 0 Here, a1 = 1, b1 = −3, c1 = −3 a2 = 3, b2 = −9, c2 = −2

So according to the question, we get a1a2a1a2 = 1313 b1b2b1b2 = −3−9−3−9 = 1313 and, c1c2c1c2 = −3−2−3−2 = 3232 ⇒ a1a2a1a2 =b1b2b1b2 ≠ c1c2c1c2

Hence, we can conclude that the given system of equation has no solution.