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If x = k2 and y = k are solutions of equation x - 5y = -6 then k =
- a)2, 3
- b)3, -2
- c)-3, 2
- d)-2, -3
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2,...
(k, k) will satisfy x -5y + 6 = 0
⇒ k2 - 5k + 6 = 0
⇒ k2 - 3k - 2k + 6 = 0
⇒ k (k -3) -2(k - 3) = 0
⇒ (k -3) (k - 2) = 0
⇒ k - 2 = 0 or, k - 3 = 0
⇒ k = 2 or 3
⇒ k2 - 5k + 6 = 0
⇒ k2 - 3k - 2k + 6 = 0
⇒ k (k -3) -2(k - 3) = 0
⇒ (k -3) (k - 2) = 0
⇒ k - 2 = 0 or, k - 3 = 0
⇒ k = 2 or 3
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If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2,...
To find the value of k in the equation x - 5y = -6, we are given that x = k^2 and y = k are solutions. We need to determine the value of k from the given options.
Given equation: x - 5y = -6
Substituting the given values of x and y:
k^2 - 5k = -6
Now, let's solve this equation step by step.
Step 1: Simplify the equation
k^2 - 5k + 6 = 0
Step 2: Factorize the quadratic equation
(k - 2)(k - 3) = 0
Step 3: Apply zero product property
k - 2 = 0 or k - 3 = 0
Step 4: Solve for k
k = 2 or k = 3
Therefore, we have two possible values for k: 2 and 3.
Now, let's check which value(s) satisfy the given equation x - 5y = -6.
For k = 2:
x = k^2 = 2^2 = 4
y = k = 2
Substituting these values in the equation:
4 - 5(2) = -6
4 - 10 = -6
-6 = -6
The equation is satisfied for k = 2.
For k = 3:
x = k^2 = 3^2 = 9
y = k = 3
Substituting these values in the equation:
9 - 5(3) = -6
9 - 15 = -6
-6 = -6
The equation is satisfied for k = 3.
Therefore, the correct answer is option A) 2, 3. Both values of k satisfy the given equation x - 5y = -6.
Given equation: x - 5y = -6
Substituting the given values of x and y:
k^2 - 5k = -6
Now, let's solve this equation step by step.
Step 1: Simplify the equation
k^2 - 5k + 6 = 0
Step 2: Factorize the quadratic equation
(k - 2)(k - 3) = 0
Step 3: Apply zero product property
k - 2 = 0 or k - 3 = 0
Step 4: Solve for k
k = 2 or k = 3
Therefore, we have two possible values for k: 2 and 3.
Now, let's check which value(s) satisfy the given equation x - 5y = -6.
For k = 2:
x = k^2 = 2^2 = 4
y = k = 2
Substituting these values in the equation:
4 - 5(2) = -6
4 - 10 = -6
-6 = -6
The equation is satisfied for k = 2.
For k = 3:
x = k^2 = 3^2 = 9
y = k = 3
Substituting these values in the equation:
9 - 5(3) = -6
9 - 15 = -6
-6 = -6
The equation is satisfied for k = 3.
Therefore, the correct answer is option A) 2, 3. Both values of k satisfy the given equation x - 5y = -6.
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If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2, 3b)3, -2c)-3, 2d)-2, -3Correct answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2, 3b)3, -2c)-3, 2d)-2, -3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2, 3b)3, -2c)-3, 2d)-2, -3Correct answer is option 'A'. Can you explain this answer?.
If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2, 3b)3, -2c)-3, 2d)-2, -3Correct answer is option 'A'. Can you explain this answer? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2, 3b)3, -2c)-3, 2d)-2, -3Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x = k2 and y = k are solutions of equation x - 5y = -6 then k =a)2, 3b)3, -2c)-3, 2d)-2, -3Correct answer is option 'A'. Can you explain this answer?.
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