Question

Solve the following simultaneous equations using Cramer’s rule.

4x + 3y – 4 = 0 ; 6x = 8 – 5y

Answer 1

4x + 3y – 4 = 0

6x = 8 – 5y

Write the given equations in the form ax + by = c
4x + 3y = 4 
6x + 5y = 8

D = `|(4, 3), (6, 5)| = 4 × 5  - 3 × 6 = 20 - 18 = 2`

D_x = `|(4, 3), (8, 5)| = 4 × 5 - 3 × 8 = 20 - 24 = - 4`

D_y = `|(4, 4), (6, 8)| = 4 × 8 - 4 × 6 = 32 - 24 = 8`

By using Cramer’s Rule,

x = `"D"_x/"D" = (-4)/2 = -2`

y = `"D"_y/"D" = (8)/2 = 4`

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