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

1.	Solve the following simultaneous equations. i. 2x – y = 5 ; 3x + 2y = 11 ii. x – 2y – 2 ; x + 2y = 10
Answer» i. 2x – y = 5 ∴ -y = 5 – 2x ∴ y = 2x – 5 …(i) 3x + 2y = 11 ……(ii) Substituting y = 2x – 5 in equation (ii), 3x + 2(2x – 5) = 11 ∴ 3x + 4x- 10= 11 ∴ 7x = 11 + 10 ∴ 7x = 21 ∴ x = \(\frac{21}{7}\) ∴ x = 3 Substituting x = 3 in equation (i), y = 2x – 5 ∴ y = 2(3) – 5 ∴ y = 6 – 5 = 1 ∴(3,1) is the solution of the given equations. ii. x – 2y = -2 ∴ x = 2y – 2 …(i) x + 2y = 10 …..(ii) Substituting x = 2y – 2 in equation (ii), 2y – 2 + 2y = 10 ∴ 4y = 10 + 2 ∴ 4y= 12 ∴ y = \(\frac{12}{4}\) ∴ y = 3 Substituting y = 3 in equation (i), x = 2y – 2 ∴ x = 2(3) – 2 ∴ x = 6 – 2 = 4 ∴ (4, 3) is the solution of the given equations

Solve the following simultaneous equations. i. 2x – y = 5 ; 3x + 2y = 11 ii. x – 2y – 2 ; x + 2y = 10

Answer»

i. 2x – y = 5

∴ -y = 5 – 2x

∴ y = 2x – 5 …(i)

3x + 2y = 11 ……(ii)

Substituting y = 2x – 5 in equation (ii),

3x + 2(2x – 5) = 11

∴ 3x + 4x- 10= 11

∴ 7x = 11 + 10

∴ 7x = 21

∴ x = \(\frac{21}{7}\)

∴ x = 3

Substituting x = 3 in equation (i),

y = 2x – 5

∴ y = 2(3) – 5

∴ y = 6 – 5 = 1

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

ii. x – 2y = -2

∴ x = 2y – 2 …(i)

x + 2y = 10 …..(ii)

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

2y – 2 + 2y = 10

∴ 4y = 10 + 2

∴ 4y= 12

∴ y = \(\frac{12}{4}\)

∴ y = 3

Substituting y = 3 in equation (i),

x = 2y – 2

∴ x = 2(3) – 2

∴ x = 6 – 2 = 4

∴ (4, 3) is the solution of the given equations