Question

Solve the following simultaneous equations using Cramer’s rule.

6x – 4y = –12; 8x – 3y = –2

Answer 1

Given equations,
6x – 4y = –12
8x – 3y = –2

D = `|(6, – 4), (8, – 3)| = 6 × (– 3)  – (– 4) × 8 = – 18 + 32 = 14`

D_x = `|(–12, – 4), (–2, – 3)| = (–12) × (– 3)  – (– 4) × (–2) = 36  –  8 = 28`

D_y = `|(6, –12), (8, – 2)| = 6 × (– 2)  – (– 12) × 8 = – 12 + 96 = 84`

By using Cramer’s rule,

x = `"D"_x/"D" = 28/14 = 2`

 

y = `"D"_y/"D" = 84/14 = 6`

 

(x, y) = (2, 6) is the solution of given equation.