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The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for
- a)α not equal to 0
- b)all integral α
- c)all rational α
- d)all real α
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2...
The given system of equations has unique solution , if
⇒1(18−2)−1(9−α) ⇒13−5α ≠ 0 ⇒ α ≠ 13/5 + 1(6−6α) ≠ 0
Therefore , unique solution exists for all integral values of α.
⇒1(18−2)−1(9−α) ⇒13−5α ≠ 0 ⇒ α ≠ 13/5 + 1(6−6α) ≠ 0
Therefore , unique solution exists for all integral values of α.
Most Upvoted Answer
The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2...
To solve this system of equations, we can use the method of substitution.
From the first equation, we have:
x + y + z = 1 ---> Equation (1)
From the second equation, we have:
3x + 6y + z = 8 ---> Equation (2)
Let's solve Equation (1) for x:
x = 1 - y - z
Now substitute this value of x in Equation (2):
3(1 - y - z) + 6y + z = 8
Expand and simplify:
3 - 3y - 3z + 6y + z = 8
3y - 2z = 5 ---> Equation (3)
Now we have two equations:
Equation (1): x + y + z = 1
Equation (3): 3y - 2z = 5
We can solve this system of equations using any method we prefer: substitution, elimination, or matrices. Let's use the substitution method:
From Equation (1), we can solve for x:
x = 1 - y - z
Substitute this value of x in Equation (3):
3y - 2z = 5
Now we have two equations:
Equation (3): 3y - 2z = 5
Equation (4): x = 1 - y - z
Now we can solve these two equations simultaneously to find the values of x, y, and z.
From the first equation, we have:
x + y + z = 1 ---> Equation (1)
From the second equation, we have:
3x + 6y + z = 8 ---> Equation (2)
Let's solve Equation (1) for x:
x = 1 - y - z
Now substitute this value of x in Equation (2):
3(1 - y - z) + 6y + z = 8
Expand and simplify:
3 - 3y - 3z + 6y + z = 8
3y - 2z = 5 ---> Equation (3)
Now we have two equations:
Equation (1): x + y + z = 1
Equation (3): 3y - 2z = 5
We can solve this system of equations using any method we prefer: substitution, elimination, or matrices. Let's use the substitution method:
From Equation (1), we can solve for x:
x = 1 - y - z
Substitute this value of x in Equation (3):
3y - 2z = 5
Now we have two equations:
Equation (3): 3y - 2z = 5
Equation (4): x = 1 - y - z
Now we can solve these two equations simultaneously to find the values of x, y, and z.
Community Answer
The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2...
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Question Description
The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2 y + 3z = 1 has a unique solution fora)α not equal to 0b)all integralαc)all rationalαd)all realαCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2 y + 3z = 1 has a unique solution fora)α not equal to 0b)all integralαc)all rationalαd)all realαCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2 y + 3z = 1 has a unique solution fora)α not equal to 0b)all integralαc)all rationalαd)all realαCorrect answer is option 'B'. Can you explain this answer?.
The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2 y + 3z = 1 has a unique solution fora)α not equal to 0b)all integralαc)all rationalαd)all realαCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2 y + 3z = 1 has a unique solution fora)α not equal to 0b)all integralαc)all rationalαd)all realαCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The system of equations, x + y + z = 1, 3 x + 6 y + z = 8,αx + 2 y + 3z = 1 has a unique solution fora)α not equal to 0b)all integralαc)all rationalαd)all realαCorrect answer is option 'B'. Can you explain this answer?.
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