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The system of linear equations 4x + 2y =7, 2x + y = 6 has
- a)a unique solution
- b)no solution
- c)an infinite number of solutions
- d)exactly two distinct solutions
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The system of linear equations 4x + 2y =7, 2x + y = 6 hasa)a unique so...
Explanation:
To determine whether the given system of linear equations has a solution, no solution, or an infinite number of solutions, we can use various methods such as substitution, elimination, or matrix representation. Let's solve the given system of equations using the elimination method.
The given system of equations is:
Equation 1: 4x + 2y = 7
Equation 2: 2x + y = 6
Step 1: Multiply Equation 2 by 2
By multiplying Equation 2 by 2, we can eliminate the variable "y" when we add the two equations together.
2 * (2x + y) = 2 * 6
4x + 2y = 12
Now, we have the following system of equations:
Equation 1: 4x + 2y = 7
Equation 2: 4x + 2y = 12
Step 2: Subtract Equation 1 from Equation 2
When we subtract Equation 1 from Equation 2, we eliminate the variable "x".
(4x + 2y) - (4x + 2y) = 12 - 7
0 = 5
We end up with the equation 0 = 5, which is not possible. This means that there is no solution that satisfies both equations simultaneously.
Conclusion:
Since the system of equations has no solution, the correct answer is option B - "no solution".
To determine whether the given system of linear equations has a solution, no solution, or an infinite number of solutions, we can use various methods such as substitution, elimination, or matrix representation. Let's solve the given system of equations using the elimination method.
The given system of equations is:
Equation 1: 4x + 2y = 7
Equation 2: 2x + y = 6
Step 1: Multiply Equation 2 by 2
By multiplying Equation 2 by 2, we can eliminate the variable "y" when we add the two equations together.
2 * (2x + y) = 2 * 6
4x + 2y = 12
Now, we have the following system of equations:
Equation 1: 4x + 2y = 7
Equation 2: 4x + 2y = 12
Step 2: Subtract Equation 1 from Equation 2
When we subtract Equation 1 from Equation 2, we eliminate the variable "x".
(4x + 2y) - (4x + 2y) = 12 - 7
0 = 5
We end up with the equation 0 = 5, which is not possible. This means that there is no solution that satisfies both equations simultaneously.
Conclusion:
Since the system of equations has no solution, the correct answer is option B - "no solution".
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Community Answer
The system of linear equations 4x + 2y =7, 2x + y = 6 hasa)a unique so...
Here, 4x + 2y = 7 and 2x + y = 6
[4 2 ] = [ 7]
[ 2 1 ] [ 6]
R1 : R1- 2R2
[ 0 0 ] = [ - 5 ]
[ 2 1] [ 6 ]
here In left side only one row and in right side is 2 row
so A < b="" is="" no="" solution="" />
# if A> B then a unique solution
# if A = B then is infinite number of solution.
[4 2 ] = [ 7]
[ 2 1 ] [ 6]
R1 : R1- 2R2
[ 0 0 ] = [ - 5 ]
[ 2 1] [ 6 ]
here In left side only one row and in right side is 2 row
so A < b="" is="" no="" solution="" />
# if A> B then a unique solution
# if A = B then is infinite number of solution.
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The system of linear equations 4x + 2y =7, 2x + y = 6 hasa)a unique solutionb)no solutionc)an infinite number of solutionsd)exactly two distinct solutionsCorrect answer is option 'B'. Can you explain this answer?
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