Question

Solve the following simultaneous equations using Cramer’s rule.
2x + 3y = 2; x - `y/2 = 1/2`.

Answer 1

2x + 3y = 2; x - `y/2 = 1/2`

 

D = `|(2, 3), (1, (-1)/2)| = 2 xx (- 1/2) - 3 xx 1 = - 1 - 3 = - 4`

 

D_x = `|(2, 3), (1/2, (-1)/2)| = 2 xx (- 1/2) - 3 xx 1/2 = - 1/1 - 3/2 =  (-2 -3)/2`

 

Dx = `(-5)/2`

 

D_y = `|(2, 2), (1, 1/2)| = 2 xx 1/2 - 2 xx 1 = 1 - 2`

 

Dy = -1

 

x = `("D"_x)/"D" = ((-5)/2)/(-4) = (-5)/2 xx 1/-4 = (-5)/-8`

 

x = `5/8`

 

y = `("D"_y)/"D" = (-1)/(-4) = 1/4.`

 

(x, y) = `(5/8, 1/4)`.