Question

ਜੇਕਰ ਦਿੱਤੇ ਗਏ ਰੇਖੀ ਸਮੀਕਰਨਾਂ ਦੇ ਜੋੜੇ cx – y = 2 ਅਤੇ 6x – 2y = 4 ਦੇ ਅਨੰਤ ਹੱਲ ਹੋਣ, ਤਾਂ c ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ। Find out the value of c for which the pair of equations cx – y = 2 and 6x – 2y =4 will have infinitely many solutions. अगर दिए गए रेखीय समीकरणों के युग्म cx – y = 2 और 6x – 2y = 4 के अनंत अनेक हल हो तो c का मूल्य पता करें। *


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Answer 1

Question :- Find out the value of c for which the pair of equations cx – y = 2 and 6x – 2y = 4 will have infinitely many solutions.

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• A linear equation in two variables represents a straight line in 2D Cartesian plane .

• If we consider two linear equations in two variables, say :-

➻ a1x + b1y + c1 = 0

➻ a2x + b2y + c2 = 0

Then :-

✪ Both the straight lines will coincide if :-

a1/a2 = b1/b2 = c1/c2

➻ In this case , the system will have infinitely many solutions.

➻ If a consistent system has an infinite number of solutions, it is dependent and consistent.

✪ Both the straight lines will be parallel if :-

a1/a2 = b1/b2 ≠ c1/c2.

➻ In this case , the system will have no solution.

➻ If a system has no solution, it is said to be inconsistent.

✪ Both the straight lines will intersect if :-

a1/a2 ≠ b1/b2.

➻ In this case , the system will have an unique solution.

➻ If a system has at least one solution, it is said to be consistent..

Solution :-

comparing the given pair of equations cx - y - 2 = 0 and 6x - 2y - 4 = 0 with a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 we get,

• a1 = c
• b1 = (-1)
• c1 = (-2)
• a2 = 6
• b2 = (-2)
• c2 = (-4)

Now, from above told concept we know that, when pair of equations have infinitely many solutions , than,

• a1/a2 = b1/b2 = c1/c2

Putting all values we get :-

→ c/6 = (-1)/(-2) = (-2)/(-4)

→ c/6 = 1/2 = 1/2

→ c/6 = 1/2

→ 2c = 6

dividing both sides by 2,

→ c = 3 (Ans.)

Hence, value of c is 3 for which given pair of equations have infinitely many solutions.

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