Solve the following simultaneous equations.i. x + y = 11 ; 2x – 3y =

1.	Solve the following simultaneous equations.i. x + y = 11 ; 2x – 3y = 7 ii. 2x + y = -2 ; 3x – y = 7
Answer» i. x + y = 11 ∴ x = 11 – y …(i) 2x – 3y = 7 …….(ii) Substituting x = 11 -y in equation (ii), 2(11 – y) – 3y = 7 ∴ 22 – 2y – 3y = 1 ∴ 22 – 5y = 7 ∴ 22 – 7 = 5y ∴ 15 = 5y ∴ y = \(\frac{15}{5}\) ∴ y = 3 Substituting y = 3 in equation (i), x = 11 – y ∴ x = 11 – 3 = 8 ∴ (8, 3) is the solution of the given equations. ii. 2x + y = -2 …(i) 3x – y = 7 …(ii) Adding equations (i) and (ii), 2x + y = -2 + 3x – y = l 5x = 5 ∴ x = \(\frac{5}{5}\) ∴ x = 1 Substituting x = 1 in equation (i), 2x + y = -2 ∴ 2(1) +y = -2 2 + y = -2 ∴ y = – 2 – 2 ∴ y = -4 ∴ (1, -4) is the solution of the given equations.

Solve the following simultaneous equations.i. x + y = 11 ; 2x – 3y = 7 ii. 2x + y = -2 ; 3x – y = 7

Answer»

i. x + y = 11

∴ x = 11 – y …(i)

2x – 3y = 7 …….(ii)

Substituting x = 11 -y in equation (ii),

2(11 – y) – 3y = 7

∴ 22 – 2y – 3y = 1

∴ 22 – 5y = 7

∴ 22 – 7 = 5y

∴ 15 = 5y

∴ y = \(\frac{15}{5}\)

∴ y = 3

Substituting y = 3 in equation (i),

x = 11 – y

∴ x = 11 – 3 = 8

∴ (8, 3) is the solution of the given equations.

ii. 2x + y = -2 …(i)

3x – y = 7 …(ii)

Adding equations (i) and (ii),

2x + y = -2

+ 3x – y = l

5x = 5

∴ x = \(\frac{5}{5}\)

∴ x = 1

Substituting x = 1 in equation (i),

2x + y = -2

∴ 2(1) +y = -2

2 + y = -2

∴ y = – 2 – 2

∴ y = -4

∴ (1, -4) is the solution of the given equations.