Question

find the value of x-y, if 17x + 12y = 68 and 12x + 17y = 48

Answer 1

$<b>Answer :</b>$

4




$<b>Step-by-step explanation :</b>$

17x + 12y = 68 _____ ( 1 )

12x + 17y = 48 ______( 2 )

$<u>Add both these equations</u>$

29x + 29y = 116

29 ( x + y ) = 116

$<i>x + y = 4</i>$ ______ ( 3 )

$<u>Subtract both these equations</u>$

5x - 5y = 20

5 ( x - y ) = 20

$<i>x - y = 4</i>$ _______ ( 4 )

Add ( 3 ) & ( 4 )

2x = 8

x = 4

Put this value in ( 4 )

4 - y = 4

y = 0

Value of x - y

= 4 - 0

$<b>= 4</b>$

Answer 2

$\binom{17x + 12y = 68}{12x + 17y = 48} \\ \\ solve \: for \: x \\ \\ \binom{x = 4 - \frac{12}{17} y}{12x + 17y = 48} \\ \\ substitute \: the \: value \: of \: x \: in \: equation \: \\ 12x + 17y = 48 \\ \\ 12( 4 - \frac{12}{17} y) + 17y = 48$


$solve \: for \: y \\ \\ 48 - \frac{144}{17} y + 17y = 48 \\ \\ - \frac{144}{17} y + 17y = 0 \\ \\ \frac{145}{17} y = 0 \\ \\ multiply \: both \: sides \: by \: \frac{17}{145} \\ \\ y = 0$

$substitute \: the \: value \: of \: y \: in \: equation \\ x = 4 - \frac{12}{17} y \\ \\ x = 4 - \frac{12}{17} \times 0 \\ \\ x = 4$

So, x = 4

and y = 0

Therefore

x - y

=> 4 - 0 = 4 ans.