Solve the set of simultaneous equations. x + y = 4 ; 2x – 5y = 1

1.	Solve the set of simultaneous equations. x + y = 4 ; 2x – 5y = 1
Answer» Substitution Method: x + y = 4 ∴ x = 4 – y …(i) 2x – 5y = 1 ……(ii) Substituting x = 4 – y in equation (ii), 2(4 – y) – 5y = 1 ∴ 8 – 2y – 5y = 1 ∴ 8 – 7y = 1 ∴ 8 – 1 = 7y ∴ 7 = 7y ∴ y = 7/7 ∴ y = 1 Substituting y = 1 in equation (i) , x = 4 – 1 = 3 ∴ (3,1) is the solution of the given equations. Alternate method: Elimination Method: x + y = 4 …(i) 2x – 5y = 1 ……(ii) Multiplying equation (i) by 5, 5x + 5y = 20 … (iii) Adding equations (ii) and (iii) , 2x – 5y = 1 + 5x + 5y = 20 7 = 21 ∴ x = 21/7 ∴ x = 3 Substituting x = 3 in equation (i), 3 + y = 4 ∴ y = 4 – 3 = 1 (3,1) is the solution of the given equations.

Answer»

Substitution Method:

x + y = 4

∴ x = 4 – y …(i)

2x – 5y = 1 ……(ii)

Substituting x = 4 – y in equation (ii),

2(4 – y) – 5y = 1

∴ 8 – 2y – 5y = 1

∴ 8 – 7y = 1

∴ 8 – 1 = 7y

∴ 7 = 7y

∴ y = 7/7

∴ y = 1

Substituting y = 1 in equation (i)

, x = 4 – 1 = 3

∴ (3,1) is the solution of the given equations.

Alternate method:

Elimination Method:

x + y = 4 …(i)

2x – 5y = 1 ……(ii)

Multiplying equation (i) by 5,

5x + 5y = 20 … (iii)

Adding equations (ii) and (iii)

, 2x – 5y = 1 + 5x + 5y = 20

7 = 21

∴ x = 21/7

∴ x = 3

Substituting x = 3 in equation (i),

3 + y = 4

∴ y = 4 – 3 = 1

(3,1) is the solution of the given equations.

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