Question

Solve the following by substitution method.

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Answer 1

(1)

The given equation are

• 3x + 5y = 6 .....(i)
• 9x - 15y = - 6 .....(ii)

From (i), we get

3x = 6 - 5y

⇒ x = (6 - 5y)/3 .....(iii)

By substituting x = (6 - 5y)/3 in (ii) no. equation, we get

9 (6 - 5y)/3 - 15y = - 6

⇒ 3 (6 - 5y) - 15y = - 6

⇒ 18 - 15y - 15y = - 6

⇒ 30y = 24

⇒ y = 24/30

⇒ y = 4/5

Putting y = 4/5 in (iii), we get

x = {6 - 5 (4/5)}/3

⇒ x = (6 - 4)/3

⇒ x = 2/3

Therefore, the required solution is

x = 2/3, y = 4/5

(2)

The given equations are

• 3x + 2y = 4 .....(i)
• 4x - y = - 13 ....(ii)

From (ii), we get

- y = - 13 - 4x

⇒ y = 4x + 13 .....(iii)

Substituting y = 4x + 13 in (i) no. equation, we get

3x + 2 (4x + 13) = 4

⇒ 3x + 8x + 26 = 4

⇒ 11x = - 22

⇒ x = - 2

Putting x = - 2 in (iii), we get

y = 4 (- 2) + 13

⇒ y = - 8 + 13

⇒ y = 5

Therefore, the required solution is

x = - 2 , y = 5

Answer 2

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