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 = ${\displaystyle \left|\begin{array}{cc}7& 3\\ -5& 12\end{array}\right|}$

= 7 × 12 − (−5) × 3

= 84 + 15

= 99

D_x = ${\displaystyle \left|\begin{array}{cc}15& 3\\ 39& 12\end{array}\right|}$

= 15 × 12 − 39 × 3

= 180 − 117

= 63

D_y = ${\displaystyle \left|\begin{array}{cc}7& 15\\ -5& 39\end{array}\right|}$

= 7 × 39 − (−5) × 15 

= 273 + 75

= 348

x = ${\displaystyle \frac{{\text{D}}_{\text{x}}}{\text{D}}=\frac{63}{99}=\frac{7}{11}}$

y = ${\displaystyle \frac{{\text{D}}_{\text{y}}}{\text{D}}=\frac{348}{99}=\frac{116}{33}}$

(x, y) = ${\displaystyle (\frac{7}{11},\frac{116}{33})}$