Question

3x-5y=16 , x-3y=8
solve the simultance equation​

Answer 1

Answer:

Value of x = 2

And value of y = - 2

Step-by-step explanation:

★ Given that:

Equation (i):→ 3x - 5y = 16

→ 3x = 16 + 5y

→ x = (16 + 5y)/3

Equation (ii):→ x - 3y = 8

→ x = 8 + 3y

Comparing both the equation:

→ (16 + 5y)/3 = 8 + 3y

→ 16 + 5y = 3(8 + 3y)

→ 16 + 5y = 24 + 9y

→ 5y - 9y = 24 - 16

→ - 4y = 8

→ y = 8/-4

→ y = - 2

∴ We get the value of y = - 2

Substituting the value of y in Equation (i) or Equation (ii):

→ x = (16 + 5 × - 2)/3

→ x = (16 - 10)/3

→ x = 6/3

→ x = 2

Or,

→ x = 8 + 3 × - 2

→ x = 8 - 6

→ x = 2

∴ We get the value of x = 2

★ Verification:

We have to verify both the equation by putting the value of x and y:

Equation (i):→

➼ 3x - 5y = 16

➼ 3(2) - 5(-2) = 16

➼ 6 + 10 = 16

Verified

Equation (ii):→

➼ x - 3y = 8

➼ 2 - 3(-2) = 8

➼ 2 + 6 = 8

Verified

Answer 2

Answer:

Required Answer :-

3x - 5y = 16 (Eqⁿ 1)

3x = 16 + 5y

x = 16 + 5y/3

x - 3y = 8 (Eqⁿ 2)

x = 8 + 3y

Now,

$\begin{gathered} \sf \: \frac{16 + 5y}{3} = 8 + 3y \end{gathered}$

$\sf \: 16 + 5y = 3(8 + 3y)$

$\sf \: 16 + 5y = 24 + 9y$

$\sf \: 5y - 9y = 24 - 16$

$\sf \: - 4y = 8$

$\sf \: y = - 2$

Now,

Finding x

$\sf \: x \: = 8 + 3( - 2)$

$\sf \: x \: = 8 - 6$

$\sf \: x \: = 2$