Question

If 15x+17y=21 and 17x+15y=11, then find the value of x+y​

Answer 1

Answer:

If we multiply the first equation by 17 and the second one by 15, we get,

255x + 289y = 357 and 255x + 225y = 165

Now, subtract both the equations..

64y = 192

y = 3

Now we can find the value of x,

15x + 17(3) = 21

15x + 51 = 21

x = -30/15

x = -2

x + y = -2+ 3 = 1

Answer 2

GIVEN :–

$\\ \: \: { \huge{.}} \: \: { \bold{15x + 17y = 21}}$

$\\ \: \: { \huge{.}} \: \: { \bold{17x + 15y = 11}}$

TO FIND :–

$\\ \: \: { \huge{.}} \: \: { \bold{value \: \: of \: \: (x + y )= ?}}$

SOLUTION :–

• According to the first condition –

$\\ \implies { \bold{15x + 17y = 21}}$

$\\ \implies { \bold{15x = 21 - 17y}}$

$\\ \implies { \bold{x = \dfrac{1}{15}(21 - 17y) \: \: \: \: - - - eq.(1)}}$

• According to the second condition –

$\\ \implies { \bold{17x + 15y = 11}}$

• Using eq.(1) –

$\\ \implies { \bold{17 \left\{\dfrac{1}{15}(21 - 17y) \right\} + 15y = 11}}$

$\\ \implies { \bold{\dfrac{17}{15}(21 - 17y) + 15y = 11}}$

$\\ \implies { \bold{\dfrac{17 \times 21}{15} -\dfrac{17 \times 17y}{15}+ 15y = 11}}$

$\\ \implies { \bold{\dfrac{357}{15} -\dfrac{289y}{15}+ 15y = 11}}$

$\\ \implies { \bold{\dfrac{357}{15} + \dfrac{225y - 289y}{15}= 11}}$

$\\ \implies { \bold{ - \dfrac{64y}{15}= 11 - \dfrac{357}{15} }}$

$\\ \implies { \bold{ - \dfrac{64y}{15}= \dfrac{165 - 357}{15} }}$

$\\ \implies { \bold{ - 64y= - 192}}$

$\\ \implies { \bold{ y= \cancel\dfrac{192}{64}}}$

$\\ \: \dashrightarrow \: \large { \boxed{ \bold{ y= 3}}}$

• Put the value of 'y' in eq.(1) –

$\\ \implies { \bold{x = \dfrac{1}{15}(21 - 17 \times 3)}}$

$\\ \implies { \bold{x = \dfrac{1}{15}(21 - 51)}}$

$\\ \implies { \bold{x = - \cancel\dfrac{30}{15}}}$

$\\ \implies \large{ \boxed { \bold{x = - 2}}}$

▪︎ Hence –

$\\ \implies { \bold{x + y=-2 + 3}}$

$\\ \: \dashrightarrow \: \large{ \boxed{ \bold{x + y=-1}}}$