Question

Solve the following simultaneous equation using Cramer's rule 

4x + 3y = 4
6x + 5y = 8

Answer 1

4x + 3y = 4 and 6x + 5y = 8

Let D = `|(4,3), (6,5)|` 

= 4 x 5 - 6 x 3

= 20 - 18

D = 2 .......(i)

Dx = `|(4,3), (8,5)|`

= 4 x 5 - 8 x 3

= 20 - 24

Dx = -4..............(ii) 

Dy = `|(4,4), (6,8)|` 

= 4 x 8 - 6 x 4

= 32 - 24

Dy = 8 ........(iii)

By cramer's rule

x = `"Dx"/"D" = (-4)/2` [from equation (i) and (ii)]

x = -2

y = `"Dy"/"D" = 8/2`

y = 4

`therefore` x = -2 and y = 4