Question

Solve the following simultaneous equations using Cramer’s rule. 

i. 3x – 4y = 10 ; 4x + 3y = 5 

ii. 4x + 3y – 4 = 0 ; 6x = 8 – 5y 

iii. x + 2y = -1 ; 2x – 3y = 12

Answer 1

i. The given simultaneous equations are 3x – 4y = 10 …(i)
4x + 3y = 5 …(ii)

Equations (i) and (ii) are in ax + by = c form. Comparing the given equations with
a₁ x + b₁ y = c₁ and a₂ x + b₂ y = c₂ , we get

a₁ = 3, b₁ = -4, c₁ = 10 and

a₂ = 4, b₂ = 3, c₂ = 5

∴ (x, y) = (2, -1) is the solution of the given simultaneous equations.

ii. The given simultaneous equations are
     4x + 3y – 4 = 0

∴ 4x + 3y = 4 …(i)

     6x = 8 – 5y

∴ 6x + 5y = 8 …(ii)

Equations (i) and (ii) are in ax + by = c form. Comparing the given equations with

a₁ x + b₁ y = c₁ and a₂ x + b₂ y = c₂ , we get

a₁ = 4, b₁ = 3, c₁ = 4 and

a₂ = 6, b₂ = 5, c₂ = 8

∴ (x, y) = (-2, 4) is the solution of the given simultaneous equations.

iii. The given simultaneous equations are

x + 2y = -1 …(i)

2x – 3y = 12 …(ii)

Equations (i) and (ii) are in ax + by = c form. Comparing the given equations with
a x + b y = C and a x + b y = c , we get

a₁ = 1, b₁ = 2, c₁ = -1 and

a₂ = 2, b₂ = -3, c₂ = 12

∴ (x, y) = (3, -2) is the solution of the given simultaneous equations.