Question

if201x+102y=504 and 102x+201y=405 the what will the value of x y​

Answer 1

Answer:

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Answer 2

$\underline{\textsf{\textbf{\purple{ \mapsto Given:}}}}$

• Two linear equations are given.
• 201x + 102y = 504
• 102x + 201y = 405

$\underline{\textsf{\textbf{\purple{ \mapsto To\:Find:}}}}$

• The value of x and y .

$\underline{\textsf{\textbf{\purple{ \mapsto Concept\:Used:}}}}$

In such cases when the co-efficients of x and y are interchanged , then firstly we add the both equations thereafter we subtract the two equations . And after that we add or subtract the two new equations .

$\underline{\textsf{\textbf{\purple{ \mapsto Answer:}}}}$

On adding both the equations :-

⇒ 201x + 102y = 504

+ 102x + 201y = 405 .

___________________

⇒ 303x + 303y = 909.

⇒303 ( x + y ) = 909.

⇒x + y = 909/303.

⇒x + y = 3 . .................................(i)

On subtracting both the equations :-

⇒ 201x + 102y = 504

- 102 x - 201y = - 405

__________________

⇒99x - 99y = 99.

⇒99 ( x - y ) = 99.

⇒ x - y = 99/99.

⇒ x - y = 1 ..................................(ii)

On adding equations (i) & (ii) :-

⇒ x + y = 3.

+ x - y = 1.

________________

⇒ 2x = 4.

⇒x = 4/2 .

⇒ x = 2 .

Put this in (i)

⇒ x+y = 3.

⇒ 2 + y = 3.

⇒ y = 3 - 2.

⇒ y = 1 .

Hence ,

$\Large\boxed{\pink{\sf \purple{\bigstar}\:x \:=\:2}}$

$\Large\boxed{\pink{\sf \purple{\bigstar}\:y \:=\:1}}$