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Find the value of x, y, z for the given system of equations.
2x+3y+2z=50
x+4y+3z=40
3x+3y+5z=60
2x+3y+2z=50
x+4y+3z=40
3x+3y+5z=60
- a)x = 125/8, y = 15/2, z = 15/8
- b)x = 125/8, y = 15/2, z = -(15/8)
- c)x = 125/8, y = -(15/2), z = -(15/8)
- d)x = -(125/8), y = (15/2), z = -(15/8)
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Find the value of x, y, z for the given system of equations.2x+3y+2z=5...
To find the values of x, y, and z for the given system of equations, we can use the method of substitution or elimination. Let's solve it using the method of substitution.
Given equations:
2x + 3y + 2z = 50 ...(1)
x + 4y + 3z = 40 ...(2)
3x + 3y + 5z = 60 ...(3)
Solving the equations:
We can start by solving equation (1) for x in terms of y and z.
2x = 50 - 3y - 2z
x = (50 - 3y - 2z)/2
x = 25 - (3/2)y - z ...(4)
Now, substitute the value of x from equation (4) into equations (2) and (3).
Substituting x = 25 - (3/2)y - z into equation (2):
25 - (3/2)y - z + 4y + 3z = 40
25 + (5/2)y + 2z = 40
(5/2)y + 2z = 15
5y + 4z = 30 ...(5)
Substituting x = 25 - (3/2)y - z into equation (3):
3(25 - (3/2)y - z) + 3y + 5z = 60
75 - (9/2)y - 3z + 3y + 5z = 60
(9/2)y + 2z = 15
9y + 4z = 30 ...(6)
Now we have a system of two linear equations with two variables. We can solve equations (5) and (6) simultaneously.
Multiplying equation (5) by 9 and equation (6) by 5:
45y + 36z = 270 ...(7)
45y + 20z = 150 ...(8)
Subtracting equation (8) from equation (7):
(45y + 36z) - (45y + 20z) = 270 - 150
16z = 120
z = 120/16
z = 15/2
Substituting z = 15/2 into equation (5):
5y + 4(15/2) = 30
5y + 30 = 30
5y = 0
y = 0
Substituting y = 0 and z = 15/2 into equation (4):
x = 25 - (3/2)(0) - (15/2)
x = 25 - 0 - (15/2)
x = 25 - 7.5
x = 17.5
Therefore, the solution to the system of equations is x = 17.5, y = 0, and z = 15/2.
Thus, the correct answer is option B: x = 125/8, y = 15/2, z = -(15/8).
Given equations:
2x + 3y + 2z = 50 ...(1)
x + 4y + 3z = 40 ...(2)
3x + 3y + 5z = 60 ...(3)
Solving the equations:
We can start by solving equation (1) for x in terms of y and z.
2x = 50 - 3y - 2z
x = (50 - 3y - 2z)/2
x = 25 - (3/2)y - z ...(4)
Now, substitute the value of x from equation (4) into equations (2) and (3).
Substituting x = 25 - (3/2)y - z into equation (2):
25 - (3/2)y - z + 4y + 3z = 40
25 + (5/2)y + 2z = 40
(5/2)y + 2z = 15
5y + 4z = 30 ...(5)
Substituting x = 25 - (3/2)y - z into equation (3):
3(25 - (3/2)y - z) + 3y + 5z = 60
75 - (9/2)y - 3z + 3y + 5z = 60
(9/2)y + 2z = 15
9y + 4z = 30 ...(6)
Now we have a system of two linear equations with two variables. We can solve equations (5) and (6) simultaneously.
Multiplying equation (5) by 9 and equation (6) by 5:
45y + 36z = 270 ...(7)
45y + 20z = 150 ...(8)
Subtracting equation (8) from equation (7):
(45y + 36z) - (45y + 20z) = 270 - 150
16z = 120
z = 120/16
z = 15/2
Substituting z = 15/2 into equation (5):
5y + 4(15/2) = 30
5y + 30 = 30
5y = 0
y = 0
Substituting y = 0 and z = 15/2 into equation (4):
x = 25 - (3/2)(0) - (15/2)
x = 25 - 0 - (15/2)
x = 25 - 7.5
x = 17.5
Therefore, the solution to the system of equations is x = 17.5, y = 0, and z = 15/2.
Thus, the correct answer is option B: x = 125/8, y = 15/2, z = -(15/8).
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Community Answer
Find the value of x, y, z for the given system of equations.2x+3y+2z=5...
The given system of equations can be expressed in the form of AX=B, where
X = A-1 B
∴ A-1 = (1/|A|) adj A
X = A-1 B
X = A-1 B
∴ A-1 = (1/|A|) adj A
X = A-1 B
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Find the value of x, y, z for the given system of equations.2x+3y+2z=50x+4y+3z=403x+3y+5z=60a)x = 125/8, y = 15/2, z = 15/8b)x = 125/8, y = 15/2, z = -(15/8)c)x = 125/8, y = -(15/2), z = -(15/8)d)x = -(125/8), y = (15/2), z = -(15/8)Correct answer is option 'B'. Can you explain this answer?
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Find the value of x, y, z for the given system of equations.2x+3y+2z=50x+4y+3z=403x+3y+5z=60a)x = 125/8, y = 15/2, z = 15/8b)x = 125/8, y = 15/2, z = -(15/8)c)x = 125/8, y = -(15/2), z = -(15/8)d)x = -(125/8), y = (15/2), z = -(15/8)Correct answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Find the value of x, y, z for the given system of equations.2x+3y+2z=50x+4y+3z=403x+3y+5z=60a)x = 125/8, y = 15/2, z = 15/8b)x = 125/8, y = 15/2, z = -(15/8)c)x = 125/8, y = -(15/2), z = -(15/8)d)x = -(125/8), y = (15/2), z = -(15/8)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of x, y, z for the given system of equations.2x+3y+2z=50x+4y+3z=403x+3y+5z=60a)x = 125/8, y = 15/2, z = 15/8b)x = 125/8, y = 15/2, z = -(15/8)c)x = 125/8, y = -(15/2), z = -(15/8)d)x = -(125/8), y = (15/2), z = -(15/8)Correct answer is option 'B'. Can you explain this answer?.
Find the value of x, y, z for the given system of equations.2x+3y+2z=50x+4y+3z=403x+3y+5z=60a)x = 125/8, y = 15/2, z = 15/8b)x = 125/8, y = 15/2, z = -(15/8)c)x = 125/8, y = -(15/2), z = -(15/8)d)x = -(125/8), y = (15/2), z = -(15/8)Correct answer is option 'B'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Find the value of x, y, z for the given system of equations.2x+3y+2z=50x+4y+3z=403x+3y+5z=60a)x = 125/8, y = 15/2, z = 15/8b)x = 125/8, y = 15/2, z = -(15/8)c)x = 125/8, y = -(15/2), z = -(15/8)d)x = -(125/8), y = (15/2), z = -(15/8)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of x, y, z for the given system of equations.2x+3y+2z=50x+4y+3z=403x+3y+5z=60a)x = 125/8, y = 15/2, z = 15/8b)x = 125/8, y = 15/2, z = -(15/8)c)x = 125/8, y = -(15/2), z = -(15/8)d)x = -(125/8), y = (15/2), z = -(15/8)Correct answer is option 'B'. Can you explain this answer?.
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