Question
Solve the following equations by Cramer’s method.
7x + 3y = 15; 12y – 5x = 39
7x + 3y = 15; 12y – 5x = 39
✓
Answer
$D=\left[\begin{array}{cc}7 & 3 \\ -5 & 12\end{array}\right]=(7 \times 12)-(3 \times-5)=84+15=99$
$D_x=\left[\begin{array}{cc}15 & 3 \\ 39 & 12\end{array}\right]=(15 \times 12)-(3 \times 39)=180-117=63$
$ D_y=\left[\begin{array}{cc}7 & 15 \\ -5 & 39\end{array}\right]=(7 \times 39)-(15 \times-5)=273+75=348 $
$x=\frac{D_x}{D}=\frac{63}{99}=\frac{7}{11} y=\frac{D_y}{D}=\frac{348}{99}=\frac{116}{33} $
$ \therefore(x, y)=\left(\frac{7}{11}, \frac{116}{33}\right)$
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