Question

Ifx (3,2) + y (2, 3) = (17, 13), find the real values
of x and y.​

Answer 1

SOLUTION

GIVEN

x(3,2) + y (2, 3) = (17, 13)

TO DETERMINE

The value of x and y

EVALUATION

Here it is given that

x(3,2) + y (2, 3) = (17, 13)

$\sf{ \implies \: (3x,2x) + (2y,3y) = (17,13)}$

$\sf{ \implies \: (3x + 2y,2x + 3y) = (17,13)}$

Comparing both sides we get

3x + 2y = 17 - - - - (1)

2x + 3y = 13 - - - - - (2)

3 × Equation 1 - 2 × Equation 2 gives

9x - 4x = 51 - 26

$\sf{ \implies \:5x =25 }$

$\sf{ \implies \:x =5 }$

Equation 1 gives

2y = 17 - ( 3 × 5 )

$\sf{ \implies \:2y =17 - 15 }$

$\sf{ \implies \:2y =2 }$

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

FINAL ANSWER

Hence the required value

x = 5 , y = 1

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