Question

3x+5y=487,5x+3y=561 find the value of X and y​

Answer 1

GIVEN :-

• 3x + 5y = 487 , 5x + 3y = 561.

TO FIND :-

• The value of x and y.

SOLUTION :-

⇒ 3x + 5y = 487 ....(1)

⇒ 5x + 3y = 561 ....(2)

Now from Equation 1 we have,

⇒ 3x + 5y = 487

⇒ 3x = 487 - 5y

⇒ x = (487 - 5y)/3

Now substitute the value of x in equation 2,

⇒ 5x + 3y = 561

⇒ 5 × (487 - 5y)/3 + 3y = 561

⇒ [ 5(487 - 5y) ]/3 + 3y = 561

⇒ (2435 - 25y)/3 + 3y = 561

⇒ (2435 - 25y + 9y)/3 = 561

⇒ (2435 - 16y)/3 = 561

⇒ 2435 - 16y = 561 × 3

⇒ 2435 - 16y = 1683

⇒ -16y = 1683 - 2435

⇒ -16y = -752

⇒ 16y = 752

⇒ y = 752/16

⇒ y = 47

Now substitute the value of y in equation 1.

⇒ 3x + 5y = 487

⇒ 3x + 5 × 47 = 487

⇒ 3x + 235 = 487

⇒ 3x = 486 - 235

⇒ 3x = 252

⇒ x = 252/3

⇒ x = 84

Hence the required value of x is 84 and the required value of y is 47.

Answer 2

Answer:

Given:-

• 3x + 5y = 487.....(1)
• 5x + 3y = 561......(2)

Find:-

• Find value of x and y

Solution:-

${ \mapsto{ \rm{3x \: + \: 5y \: = 487}}}$

${ \mapsto { \rm{3x \: = 487 - 5y}}}$

${ \mapsto{ \rm \large{x = \frac{487 - 5y}{3} }}}$

So, Now substitute the value of x in second equation

${ \to{ \rm{5x \: + 3y = 561}}}$

${ \to{ \rm{5( \frac{487 - 5y}{3} ) + 3y = 561}}}$

${ \to{ \rm{ \frac{2435 - 25y}{3} + 3y = 561 }}}$

${ \to{ \rm{ \frac{2435 - 25y + 9y}{3} = 561}}}$

${ \to{ \rm{2435 - 25y + 9y = 561 \times 3}}}$

${ \to{ \rm{2435 - 16y = 1683}}}$

${ \to{ \rm{ - 16y = 1683 - 2435}}}$

${ \to{ \rm{16y = 752}}}$

${ \to{ \rm{y = \frac{752}{16} = 47 }}}$

${ \boxed{ \therefore{ \pink{ \sf{y = 47 }}}}}$

For finding the value of x let us substitute the value of y in equation (1)

${ \to{ \rm{3x + 5y = 487}}}$

${ \to{ \rm{3x + 5(47) = 487 \: }}}$

${ \to{ \rm{3x + 235 = 487}}}$

${ \to{ \rm{3x = 487 - 235}}}$

${ \to{ \rm{3x = 252}}}$

${ \to{ \rm{x = \frac{252}{3} = 84}}}$

${ \boxed { \therefore{ \pink{ \sf{x = 84}}}}}$

Therefore,

• x = 84
• y = 47