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Q.

If x=a and y=b is the solution of the equations x-y=2 and x+y=4 is the solution of the equations x-y=2 and then the values of a and b are respectively


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a

a=3 and b=5

b

a=5 and b=3

c

a=3 and b=1

d

a=-1 and b=-3 

answer is C.

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Detailed Solution

Given that x=a and y=b is the solution of the equations x-y=2.
We know that if the solution of the polynomial p(x) is x=a, then p(a)=0.
Substitute x=a and y=b in the given equations. We get,
a+b=4 ………..(1)  a−b=2 ……….(2)
Let us add the equations (1) and (2).
a−b + a+b =2+4 ⇒a−b+a+b=6   ⇒2a=6 ⇒a=3 In equation (1), substitute the value of a.
we get,  3−b=2 ⇒b=1 As a result, a and b have values of 3 and 1, respectively.
The correct option is (1).
 
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If x=a and y=b is the solution of the equations x-y=2 and x+y=4 is the solution of the equations x-y=2 and then the values of a and b are respectively