Question

solve the following pairs of linear equation by the method of of substitution 5x -3y = 0 , 3x-5y =16




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Answer 1

Given Equations:-

• 5x - 3y = 0
• 3x - 5y = 16

To Find:-

• The value of x and y

Method used:-

• Substitution method.

Solution:-

From given we have,

• 5x - 3y = 0 ⟶ (i)
• 3x - 5y = 16 ⟶ (ii)

From equation (i)

= 5x - 3y = 0

⇒ 5x = 3y

⇒ x = 3y/5

Substituting the value of x in equation (ii)

= 3x - 5y = 16

⇒ 3(3y/5) - 5y = 16

⇒ 9y/5 - 5y = 16

⇒ (9y - 25y)/5 = 16

⇒ - 16y = 16 × 5

⇒ -16y = 80

⇒ y = 80/-16

⇒ y = -5

Putting the value of y in equation (i)

= 5x - 3y = 0

⇒ 5x - 3 × (-5) = 0

⇒ 5x + 15 = 0

⇒ 5x = -15

⇒ x = -15/5

⇒ x = -3

∴ The values of x and y are as follows:-

• x = -3
• y = -5

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Verification!!

Let us put the value of x and y in equation (i)

= 5x - 3y = 0

Taking LHS,

⇒ 5 × (-3) - 3 × (-5)

⇒ - 15 + 15

= 0 = RHS

Now,

Let us put the value of x and y in equation (ii)

= 3x - 5y = 16

Taking LHS,

⇒ 3 × (-3) - 5 × (-5)

⇒ -9 + 25

= 16 = (RHS)

Hence Verified!!!

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Answer 2

Question :-

• Solve the following pairs of linear equation by the method of of substitution 5x -3y = 0 , 3x-5y =16

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To Find :-

• Value of x and y

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Equations :-

• 5x - 3y = 0
• 3x - 5y = 16

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Solution :-

• Here, We have to use the substitution method as in the question

From equation 1,

5x - 3y = 0

≈ 5x = 3y

≈ x = 3y/5

• Now, we will substitute the value of x in equation 2

≈ 3x - 5y = 16

≈ 3 (3y/5) - 5y = 16

≈ 9y/15 - 5y = 16

≈ 9y - 25y/15 = 16

≈ -16y/15 = 16

≈ -16y = 16 × 15

≈ -16y = 80

≈ y = 80/-16

≈ y = -5

• Now, we have to put the value of y in equation 1

≈ 5x - 3y = 0

≈ 5x - 3 × (-5) = 0

≈ 5x + 15 = 0

≈ 5x = 0 - 15

≈ 5x = -15

≈ x = -15/5

≈ x = -3

1. x = -3
2. y = -5

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Hope that helps !!!