Question

find ordered pair of (5x-3y,3x-y)=(16,12)

Answer 1

Given :- find ordered pair of (5x-3y,3x-y) = (16,12) .

Solution :-

→ (5x-3y,3x-y) = (16,12) .

comparing we get,

→ 5x - 3y = 16 -------- Eqn.(1)

and,

→ 3x - y = 12 --------- Eqn.(2)

multiply Eqn.(2) by 3 and then subtracting both we get,

→ (5x - 3y) - 3(3zx - y) = 16 - 3 * 12

→ 5x - 9x - 3y + 3y = 16 - 36

→ (-4x) = (-20)

→ x = 5 .

putting value of x in Eqn.(2),

→ 3 * 5 - y = 12

→ 15 - y = 12

→ y = 15 - 12

→ y = 3 .

Hence, ordered pair will be x = 5 and y = 3 .

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Answer 2

SOLUTION

TO DETERMINE

The ordered pair of

( 5x - 3y , 3x - y ) = ( 16 , 12 )

EVALUATION

Here it is given that

( 5x - 3y , 3x - y ) = ( 16 , 12 )

We know that ,

(a, b) = (c, d) implies a = c and b = d

Thus ( 5x - 3y , 3x - y ) = ( 16 , 12 ) gives

5x - 3y = 16 - - - - - - (1)

3x - y = 12 - - - - - - -(2)

Now Multiplying Equation 2 by 3 we get

9x - 3y = 36 - - - - - - (3)

Equation 3 - Equation 1 gives

4x = 20

⇒ x = 5

Putting the value of x in Equation 2 we get

( 3 × 5 ) - y = 12

⇒ 15 - y = 12

⇒ - y = 12 - 15

⇒ - y = - 3

⇒ y = 3

∴ ( x , y ) = ( 5 , 3 )

We see that the solution is unique

Consequently the ordered pair is unique

FINAL ANSWER

Hence the required ordered pair is

$\boxed{ \sf{ \: (x,y) = (5,3) \: \: }}$

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