Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following system of equations:3x...
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Consider the following system of equations:
3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0
The number of solutions for this system is __________________
4x + 7z = 1
x + y + z = 3
x – 2y + 7z = 0
The number of solutions for this system is __________________
Correct answer is '1'. Can you explain this answer?
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Most Upvoted Answer
Consider the following system of equations:3x + 2y = 14x + 7z = 1x + y...
By adding 1+2
and solve all 3 equation
than we find only 1 value of x,y,z
so correct answer is 1
and solve all 3 equation
than we find only 1 value of x,y,z
so correct answer is 1
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Community Answer
Consider the following system of equations:3x + 2y = 14x + 7z = 1x + y...
To solve this system of equations, we can use the method of substitution.
First, let's solve the first equation for x:
3x - 2y = 1
3x = 2y + 1
x = (2y + 1)/3
Now, substitute x = (2y + 1)/3 into the second and third equations:
4(2y + 1)/3 + 7z = 1 (Equation 2)
(2y + 1)/3 + y + z = 3 (Equation 3)
Simplify Equation 2:
(8y + 4)/3 + 7z = 1
8y + 4 + 21z = 3
8y + 21z = -1 (Equation 4)
Simplify Equation 3:
2y + 1 + 3y + 3z = 9
5y + 3z = 8 (Equation 5)
Now, we have a system of two equations with two variables: Equation 4 and Equation 5.
Let's solve Equation 5 for y:
5y + 3z = 8
5y = 8 - 3z
y = (8 - 3z)/5
Substitute y = (8 - 3z)/5 into Equation 4:
8(8 - 3z)/5 + 21z = -1
64 - 24z + 105z = -5
81z = -69
z = -69/81
z = -23/27
Substitute z = -23/27 into Equation 5:
5y + 3(-23/27) = 8
5y - 23/9 = 8
5y = 8 + 23/9
5y = 71/9
y = (71/9)/5
y = 71/45
Finally, substitute z = -23/27 and y = 71/45 into the expression for x:
x = (2y + 1)/3
x = (2(71/45) + 1)/3
x = (142/45 + 45/45)/3
x = (187/45)/3
x = 187/135
Therefore, the solution to the system of equations is x = 187/135, y = 71/45, and z = -23/27.
First, let's solve the first equation for x:
3x - 2y = 1
3x = 2y + 1
x = (2y + 1)/3
Now, substitute x = (2y + 1)/3 into the second and third equations:
4(2y + 1)/3 + 7z = 1 (Equation 2)
(2y + 1)/3 + y + z = 3 (Equation 3)
Simplify Equation 2:
(8y + 4)/3 + 7z = 1
8y + 4 + 21z = 3
8y + 21z = -1 (Equation 4)
Simplify Equation 3:
2y + 1 + 3y + 3z = 9
5y + 3z = 8 (Equation 5)
Now, we have a system of two equations with two variables: Equation 4 and Equation 5.
Let's solve Equation 5 for y:
5y + 3z = 8
5y = 8 - 3z
y = (8 - 3z)/5
Substitute y = (8 - 3z)/5 into Equation 4:
8(8 - 3z)/5 + 21z = -1
64 - 24z + 105z = -5
81z = -69
z = -69/81
z = -23/27
Substitute z = -23/27 into Equation 5:
5y + 3(-23/27) = 8
5y - 23/9 = 8
5y = 8 + 23/9
5y = 71/9
y = (71/9)/5
y = 71/45
Finally, substitute z = -23/27 and y = 71/45 into the expression for x:
x = (2y + 1)/3
x = (2(71/45) + 1)/3
x = (142/45 + 45/45)/3
x = (187/45)/3
x = 187/135
Therefore, the solution to the system of equations is x = 187/135, y = 71/45, and z = -23/27.
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Consider the following system of equations:3x + 2y = 14x + 7z = 1x + y + z = 3x – 2y + 7z = 0The number of solutions for this system is __________________Correct answer is '1'. Can you explain this answer?
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