Solve the following simultaneous equations.i. 2x + y = 5 ; 3x – y =

1.	Solve the following simultaneous equations.i. 2x + y = 5 ; 3x – y = 5 ii. x – 2y = -1 ; 2x – y = 7
Answer» i. 2x + y = 5 …(i) 3x – y = 5 …(ii) Adding equations (i) and (ii), 2x + y = 5 3x – y = 5 5x = 10 ∴ x = 10/5 ∴ x = 2 Substituting x = 2 in equation (i), 2(2) + y = 5 4 + y = 5 ∴ y = 5 – 4 = 1 ∴ (2, 1) is the solution of the given equations. ii. x – 2y = -1 ∴x = 2y – 1 … .(i) ∴ 2x – y = 7 ….(ii) Substituting x = 2y – 1 in equation (ii), 2(2y – 1) – y = 7 ∴ 4y – 2 – y = 7 ∴ 3y = 7 + 2 ∴ 3y = 9 ∴ y = 9/3 ∴ y = 3 Substituting y = 3 in equation (i), x = 2y – 1 ∴ x = 2(3) – 1 ∴ x = 6 – 1 = 5 ∴ (5, 3) is the solution of the given equations.

Solve the following simultaneous equations.i. 2x + y = 5 ; 3x – y = 5 ii. x – 2y = -1 ; 2x – y = 7

Answer»

i. 2x + y = 5 …(i)

3x – y = 5 …(ii)

Adding equations (i) and (ii),

2x + y = 5

3x – y = 5

5x = 10

∴ x = 10/5

∴ x = 2

Substituting x = 2 in equation (i),

2(2) + y = 5

4 + y = 5

∴ y = 5 – 4 = 1

∴ (2, 1) is the solution of the given equations.

ii. x – 2y = -1

∴x = 2y – 1 … .(i)

∴ 2x – y = 7 ….(ii)

Substituting x = 2y – 1 in equation (ii),

2(2y – 1) – y = 7

∴ 4y – 2 – y = 7

∴ 3y = 7 + 2

∴ 3y = 9

∴ y = 9/3

∴ y = 3

Substituting y = 3 in equation (i),

x = 2y – 1

∴ x = 2(3) – 1

∴ x = 6 – 1 = 5

∴ (5, 3) is the solution of the given equations.