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For the following set of simultaneous equations:
1.5x – 0.5y = 2
4x + 2y + 3z = 9
7x + y + 5z = 10
1.5x – 0.5y = 2
4x + 2y + 3z = 9
7x + y + 5z = 10
- a)The solution is unique
- b)Infinitely many solutions exist
- c)The equations are incompatible
- d)Finite number of multiple solutions exist
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
For the following set of simultaneous equations:1.5x – 0.5y = 24...
(a)
∴ rank of(
) = rank of(A) = 3
) = rank of(A) = 3∴ The system has unique solution.
Most Upvoted Answer
For the following set of simultaneous equations:1.5x – 0.5y = 24...
Let's solve the given set of simultaneous equations step by step to determine the nature of the solution.
Given equations:
1.5x - 0.5y = 2 ...(1)
4x + 2y + 3z = 9 ...(2)
7x + y + 5z = 10 ...(3)
To solve these equations, we can use the method of elimination or substitution. Here, we will use the method of elimination.
Step 1: Multiply equation (1) by 2:
3x - y = 4 ...(4)
Step 2: Multiply equation (3) by 2:
14x + 2y + 10z = 20 ...(5)
Step 3: Subtract equation (4) from equation (5):
(14x + 2y + 10z) - (3x - y) = 20 - 4
11x + 3y + 10z = 16 ...(6)
Step 4: Subtract equation (2) from equation (6):
(11x + 3y + 10z) - (4x + 2y + 3z) = 16 - 9
7x + y + 7z = 7 ...(7)
Now, we have two equations:
7x + y + 7z = 7 ...(7)
7x + y + 5z = 10 ...(3)
Subtracting equation (7) from equation (3):
(7x + y + 5z) - (7x + y + 7z) = 10 - 7
-2z = 3
z = -3/2
Substituting the value of z in equation (3):
7x + y + 5(-3/2) = 10
7x + y - 15/2 = 10
7x + y = 10 + 15/2
7x + y = 20/2 + 15/2
7x + y = 35/2
y = 35/2 - 7x
Substituting the values of y and z in equation (1):
1.5x - 0.5(35/2 - 7x) = 2
1.5x - 17.5/2 + 3.5x = 2
1.5x + 3.5x = 2 + 17.5/2
5x = 4 + 17.5/2
5x = 8 + 17.5/2
5x = 16 + 17.5/2
5x = 32/2 + 17.5/2
5x = 49.5/2
x = 49.5/2 * 1/5
x = 99/20
Therefore, the solution to the given set of simultaneous equations is x = 99/20, y = 35/2 - 7x, and z = -3/2.
Since the solution contains specific values for x, y, and z, and there are no parameters or variables, the solution is unique.
Hence, the correct answer is option A) The solution is unique.
Given equations:
1.5x - 0.5y = 2 ...(1)
4x + 2y + 3z = 9 ...(2)
7x + y + 5z = 10 ...(3)
To solve these equations, we can use the method of elimination or substitution. Here, we will use the method of elimination.
Step 1: Multiply equation (1) by 2:
3x - y = 4 ...(4)
Step 2: Multiply equation (3) by 2:
14x + 2y + 10z = 20 ...(5)
Step 3: Subtract equation (4) from equation (5):
(14x + 2y + 10z) - (3x - y) = 20 - 4
11x + 3y + 10z = 16 ...(6)
Step 4: Subtract equation (2) from equation (6):
(11x + 3y + 10z) - (4x + 2y + 3z) = 16 - 9
7x + y + 7z = 7 ...(7)
Now, we have two equations:
7x + y + 7z = 7 ...(7)
7x + y + 5z = 10 ...(3)
Subtracting equation (7) from equation (3):
(7x + y + 5z) - (7x + y + 7z) = 10 - 7
-2z = 3
z = -3/2
Substituting the value of z in equation (3):
7x + y + 5(-3/2) = 10
7x + y - 15/2 = 10
7x + y = 10 + 15/2
7x + y = 20/2 + 15/2
7x + y = 35/2
y = 35/2 - 7x
Substituting the values of y and z in equation (1):
1.5x - 0.5(35/2 - 7x) = 2
1.5x - 17.5/2 + 3.5x = 2
1.5x + 3.5x = 2 + 17.5/2
5x = 4 + 17.5/2
5x = 8 + 17.5/2
5x = 16 + 17.5/2
5x = 32/2 + 17.5/2
5x = 49.5/2
x = 49.5/2 * 1/5
x = 99/20
Therefore, the solution to the given set of simultaneous equations is x = 99/20, y = 35/2 - 7x, and z = -3/2.
Since the solution contains specific values for x, y, and z, and there are no parameters or variables, the solution is unique.
Hence, the correct answer is option A) The solution is unique.
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For the following set of simultaneous equations:1.5x – 0.5y = 24...
A
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For the following set of simultaneous equations:1.5x – 0.5y = 24x + 2y + 3z = 97x + y + 5z = 10a)The solution is uniqueb)Infinitely many solutions existc)The equations are incompatibled)Finite number of multiple solutions existCorrect answer is option 'A'. Can you explain this answer?
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