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For what value of a, if any, will the following system of equations in x, y and z have a solution
2x + 3y = 4
x + y + z = 4
x + 2y - z = a
2x + 3y = 4
x + y + z = 4
x + 2y - z = a
- a)Any real number
- b)0
- c)1
- d)There is no such value
Correct answer is option 'B'. Can you explain this answer?
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For what value of a, if any, will the following system of equations in...
Augmented matrix is
will have solution if a=0 as Rank A= Rank (aug. A)
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For what value of a, if any, will the following system of equations in...
Understanding the System of Equations
We have the following system of equations:
1. 2x + 3y = 4
2. x + y + z = 4
3. x + 2y - z = a
We need to determine the value of 'a' for which this system has a solution.
Step 1: Express z in terms of x and y
From the second equation, we can express z:
- z = 4 - x - y
Step 2: Substitute z into the third equation
Now, substitute the expression for z into the third equation:
- x + 2y - (4 - x - y) = a
- This simplifies to:
2x + 3y - 4 = a
- Rearranging gives:
2x + 3y = a + 4
Step 3: Compare with the first equation
We already have the first equation:
- 2x + 3y = 4
Now, equate the two expressions for 2x + 3y:
- 4 = a + 4
Step 4: Solve for a
Solving the equation yields:
- a = 0
Conclusion: Value of a
For the system to have a solution, 'a' must equal 0. Therefore, the correct option is:
- b) 0
This indicates that when 'a' is zero, the system of equations is consistent and has at least one solution. If 'a' takes any other value, the equations would be inconsistent, leading to no solution.
We have the following system of equations:
1. 2x + 3y = 4
2. x + y + z = 4
3. x + 2y - z = a
We need to determine the value of 'a' for which this system has a solution.
Step 1: Express z in terms of x and y
From the second equation, we can express z:
- z = 4 - x - y
Step 2: Substitute z into the third equation
Now, substitute the expression for z into the third equation:
- x + 2y - (4 - x - y) = a
- This simplifies to:
2x + 3y - 4 = a
- Rearranging gives:
2x + 3y = a + 4
Step 3: Compare with the first equation
We already have the first equation:
- 2x + 3y = 4
Now, equate the two expressions for 2x + 3y:
- 4 = a + 4
Step 4: Solve for a
Solving the equation yields:
- a = 0
Conclusion: Value of a
For the system to have a solution, 'a' must equal 0. Therefore, the correct option is:
- b) 0
This indicates that when 'a' is zero, the system of equations is consistent and has at least one solution. If 'a' takes any other value, the equations would be inconsistent, leading to no solution.
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For what value of a, if any, will the following system of equations in x, y and z have a solution2x + 3y = 4x + y + z = 4x + 2y - z = aa)Any real numberb)0c)1d)There is no such valueCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about For what value of a, if any, will the following system of equations in x, y and z have a solution2x + 3y = 4x + y + z = 4x + 2y - z = aa)Any real numberb)0c)1d)There is no such valueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what value of a, if any, will the following system of equations in x, y and z have a solution2x + 3y = 4x + y + z = 4x + 2y - z = aa)Any real numberb)0c)1d)There is no such valueCorrect answer is option 'B'. Can you explain this answer?.
For what value of a, if any, will the following system of equations in x, y and z have a solution2x + 3y = 4x + y + z = 4x + 2y - z = aa)Any real numberb)0c)1d)There is no such valueCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about For what value of a, if any, will the following system of equations in x, y and z have a solution2x + 3y = 4x + y + z = 4x + 2y - z = aa)Any real numberb)0c)1d)There is no such valueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what value of a, if any, will the following system of equations in x, y and z have a solution2x + 3y = 4x + y + z = 4x + 2y - z = aa)Any real numberb)0c)1d)There is no such valueCorrect answer is option 'B'. Can you explain this answer?.
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