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If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 then what will be value of a and b
- a)2,1
- b)3,1
- c)4,6
- d)1,2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 th...
X=a. y=b
a-b=2
a=2+b_(1)
a+b=4
2+b+b=4 _from (1)
2+2b=4
2b=2
b=1
a-1=2_(b=1)
a=3
ans:(3,1)
a-b=2
a=2+b_(1)
a+b=4
2+b+b=4 _from (1)
2+2b=4
2b=2
b=1
a-1=2_(b=1)
a=3
ans:(3,1)
Most Upvoted Answer
If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 th...
To find the values of 'a' and 'b' that satisfy the given pair of equations, we can substitute the values of 'x' and 'y' with 'a' and 'b' respectively.
Given equations:
1) x - y = 2
2) xy = 4
Substituting x=a and y=b in the equations:
1) a - b = 2
2) ab = 4
We now have a system of two equations with two variables. To solve this system, we can use the method of substitution or elimination.
Using the method of substitution:
From equation 1), we can express 'a' in terms of 'b':
a = b + 2
Substituting this value of 'a' in equation 2):
(b + 2)b = 4
b^2 + 2b - 4 = 0
Now, we can solve this quadratic equation to find the value(s) of 'b'. Factoring or using the quadratic formula, we find that the solutions are:
b = -2 and b = 2
Since 'b' represents the value of 'y', it cannot be negative as it would result in a complex solution. Therefore, we discard the solution b = -2.
So, the value of 'b' is 2.
To find the value of 'a', we substitute the value of 'b' in equation 1):
a - 2 = 2
a = 4
Therefore, the solution to the system of equations is a=4 and b=2.
Hence, the correct answer is option 'B' (4, 2).
Given equations:
1) x - y = 2
2) xy = 4
Substituting x=a and y=b in the equations:
1) a - b = 2
2) ab = 4
We now have a system of two equations with two variables. To solve this system, we can use the method of substitution or elimination.
Using the method of substitution:
From equation 1), we can express 'a' in terms of 'b':
a = b + 2
Substituting this value of 'a' in equation 2):
(b + 2)b = 4
b^2 + 2b - 4 = 0
Now, we can solve this quadratic equation to find the value(s) of 'b'. Factoring or using the quadratic formula, we find that the solutions are:
b = -2 and b = 2
Since 'b' represents the value of 'y', it cannot be negative as it would result in a complex solution. Therefore, we discard the solution b = -2.
So, the value of 'b' is 2.
To find the value of 'a', we substitute the value of 'b' in equation 1):
a - 2 = 2
a = 4
Therefore, the solution to the system of equations is a=4 and b=2.
Hence, the correct answer is option 'B' (4, 2).
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Community Answer
If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 th...
X=a. y=b
a-b=2
a=2+b_(1)
a+b=4
2+b+b=4 _from (1)
2+2b=4
2b=2
b=1
a-1=2_(b=1)
a=3
ans:(3,1)
a-b=2
a=2+b_(1)
a+b=4
2+b+b=4 _from (1)
2+2b=4
2b=2
b=1
a-1=2_(b=1)
a=3
ans:(3,1)
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If x=a, y=b is the solution of the pair of equation x-y=2 and x+y=4 then what will be value of a and ba)2,1b)3,1c)4,6d)1,2Correct answer is option 'B'. Can you explain this answer?
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