Question

Solve the following equations by Cramer’s method.
7x + 3y = 15; 12y – 5x = 39

Answer 1

7x + 3y = 15; 12y – 5x = 39

   7x + 3y = 15
–5x + 12y = 39

D = `|(7,3),(-5,12)|`

= 7 × 12 − (−5) × 3

= 84 + 15

= 99

D_x = `|(15,3),(39,12)|`

= 15 × 12 − 39 × 3

= 180 − 117

= 63

D_y = `|(7,15),(-5,39)|`

= 7 × 39 − (−5) × 15 

= 273 + 75

= 348

x = `("D"_"x")/("D") = 63/99 = 7/11`

y = `("D"_"y")/("D") = 348/99 = 116/33`

(x, y) = `(7/11, 116/33)`