Question

Solve the following equations by Cramer’s method.

`3x  –  2y = 5/2; 1/3x + 3y = -4/3`

Answer 1

Given equation,

`3x  –  2y = 5/2`

`1/3x + 3y = -4/3`

D = `|(3, -2), (1/3, 3)| = 3 × 3  -  (-2) × 1/3 = 9 + 2/3 = 29/3`

 

D_x = `|(5/2, -2), (-4/3, 3)| = 5/2 × 3  -  (-2) × (-4/3) = 15/2 - 8/3 = 29/6`

 

D_y = `|(3, 5/2), (1/3, -4/3)| = 3 × (-4/3) - 5/2 × (1/3) = - 4 - 5/6 = (-29)/6`

By using cramer's method,

x = `"D"_x/"D" = (29/6)/(29/3) = 29/6 × 3/29 = 1/2`
y = `"D"_y/"D" = (-29/6)/(29/3) = (-29)/6 × 3/29 = (-1)/2`

(x, y) = `(1/2, (-1)/2)` is the solution of given equation.