Question

Solve the following simultaneous equations using Cramer’s rule.

x + 2y = –1; 2x – 3y = 12

Answer 1

x + 2y = –1; 2x – 3y = 12

D = `|(1, 2), (2, -3)|`

= 1 × (−3) − 2 × 2

= −3 − 4

= −7

D_x = `|(-1, 2), (12, -3)|`

= (−1) × (−3) − 2 × 12

= 3 − 24

= −21

D_y = `|(1, -1), (2, 12)|`

= 1 × 12 − (−1) × 2

= 12 + 2

= 14

x = `D_x/D`

= `(-21)/(-7)`

= 3

y = `D_y/D`

= `14/-7`

= −2

(x, y) = (3, −2)