Question

If x=a and y=b is the solution of pair of
equations x-y=2 and x+y=4, then values of a
Α. a=2,b=1
B. a=3, b=2
С. a=2,b=3
D. a=3, b=1​

Answer 1

Step-by-step explanation:

Answer:-

Given that:-

• x=a and y=b
• Equations on which we need to work are:-

1. x-y=2
2. x+y=4

"☆"Concept:-

Replacement of the values, either earlier or later.

[☆] Star mark used because:-

• The question can be done in 2 phases:-
• Either from chapter coordinate geometry
• Or from the chapter Algebra.

Let's Do!

If we observe the (1) and (2) equation, we will add them.

$\sf{x + y + ( x - y) = 2 + 4}$

$\sf{x + \cancel{ \: y} + x \: \: \cancel{- y} = 2 + 4}$

$\sf{2x = 6}$

$\sf{x = 3}$

Now, we will find the value of y.

We can take any Equations, I am taking equation (1) for it.

$\sf{x - y = 2}$

$\sf{3 - y = 2}$

$\sf{ \cancel{- } y = \cancel{- }1}$

$\sf{y = 1}$

So, now we know that a = x and b = y

$\sf{x = a = 3}$

$\sf{y = b = 1}$

Hence, the correct option is D.

Answer 2

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Given Question:-

If x=a and y=b is the solution of pair of

equations x-y=2 and x+y=4, then values of a

Α. a=2,b=1

B. a=3, b=2

С. a=2,b=3

D. a=3, b=1

Required Answer:-

$\implies \sf{x = a = 3}$

$\implies \sf{y = b = 1}$

$\huge{ \green{ \boxed{ \sf{ \orange{Option \: D}}}}}$

Explanation:-

$\large{ \underline{ \sf{Given:-}}}$

• x=a and y=b is the solution of pair of
• equations
• Equations:-

1. x-y=2

2. x+y=4

$\large{ \underline{ \sf{To \: Find:- }}}$

• Find the values of a and b.

$\large{ \underline{ \sf{Digging \:out:- }}}$

Lets add both the equations:-

$\implies \sf{(x - y = 2) + (x + y = 4)}$

Here y will get cancel because of opposite signs.

$\implies \sf{2x = 6}$

$\implies \sf{x = 3}$

• So the value we got for X is 3.
• Putting value of x in one equation-

$\implies \sf{x - y = 2}$

$\implies \sf{3 - y = 2}$

$\implies \sf{3 - 2 = y}$

$\implies \sf{ y = 1}$

• So, the value of y we got is 1.

So, the values of a and b, i.e.

$\implies \sf{x = a = 3}$

$\implies \sf{y = b = 1}$

$\huge{ \green{ \boxed{ \sf{ \orange{Option \: D}}}}}{ \checkmark}$

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