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Find the value of x and y for the given system of equations.
3x+4y=6
5x-4y=4
3x+4y=6
5x-4y=4
- a)x=-(5/4), y=-(16/9)
- b)x=(5/4), y=-(9/16)
- c)x=-(5/4), y= 16/9
- d)x=5/4, y=9/16
Correct answer is option 'D'. Can you explain this answer?
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Find the value of x and y for the given system of equations.3x+4y=65x-...
The given system of equations can be expressed in the form of AX=B,
⇒X=A-1 B
We know that, A-1=1/|A| adj A
⇒X=A-1 B
We know that, A-1=1/|A| adj A
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Find the value of x and y for the given system of equations.3x+4y=65x-...
To find the values of x and y for the given system of equations, we can solve the equations simultaneously using the method of elimination or substitution.
Given equations:
3x + 4y = 6 ...(1)
5x - 4y = 4 ...(2)
We will solve the equations using the method of elimination.
Elimination Method:
To eliminate the y term, we can add equations (1) and (2) together.
(3x + 4y) + (5x - 4y) = 6 + 4
8x = 10
Divide both sides by 8:
x = 10/8
x = 5/4
Substitution Method:
From equation (1), we can express x in terms of y:
3x = 6 - 4y
x = (6 - 4y)/3
Substitute this value of x into equation (2):
5(6 - 4y)/3 - 4y = 4
Multiply both sides by 3 to eliminate the fraction:
5(6 - 4y) - 12y = 12
30 - 20y - 12y = 12
Combine like terms:
30 - 32y = 12
-32y = 12 - 30
-32y = -18
Divide both sides by -32:
y = -18/-32
y = 9/16
Therefore, the solution to the given system of equations is:
x = 5/4
y = 9/16
Hence, the correct answer is option D: x = 5/4, y = 9/16.
Given equations:
3x + 4y = 6 ...(1)
5x - 4y = 4 ...(2)
We will solve the equations using the method of elimination.
Elimination Method:
To eliminate the y term, we can add equations (1) and (2) together.
(3x + 4y) + (5x - 4y) = 6 + 4
8x = 10
Divide both sides by 8:
x = 10/8
x = 5/4
Substitution Method:
From equation (1), we can express x in terms of y:
3x = 6 - 4y
x = (6 - 4y)/3
Substitute this value of x into equation (2):
5(6 - 4y)/3 - 4y = 4
Multiply both sides by 3 to eliminate the fraction:
5(6 - 4y) - 12y = 12
30 - 20y - 12y = 12
Combine like terms:
30 - 32y = 12
-32y = 12 - 30
-32y = -18
Divide both sides by -32:
y = -18/-32
y = 9/16
Therefore, the solution to the given system of equations is:
x = 5/4
y = 9/16
Hence, the correct answer is option D: x = 5/4, y = 9/16.
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Find the value of x and y for the given system of equations.3x+4y=65x-4y=4a)x=-(5/4),y=-(16/9)b)x=(5/4),y=-(9/16)c)x=-(5/4),y= 16/9d)x=5/4,y=9/16Correct answer is option 'D'. Can you explain this answer?
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