Question

Use Cramer's Rule to solve the following system: –2x – 6y = –26 5x + 2y = 13

Answer 1

By Cramer's rule, the solution can be found as the ratio of determinants. The numerator is the matrix with the right-side constants replacing the coefficients of the variable of interest. The denominator is the matrix of coefficients.

$x=\displaystyle\frac{det\left[\begin{array}{cc}-26&-6\\13&2\end{array}\right]}{det\left[\begin{array}{cc}-2&-6\\5&2\end{array}\right]}=\frac{(-26)(2)-(13)(-6)}{(-2)(2)-(5)(-6)}\\\\=\frac{26}{26}=1\\\\y=\frac{det\left[\begin{array}{cc}-2&-26\\5&13\end{array}\right]}{26}=\frac{(-2)(13)-(5)(-26)}{26}\\\\=\frac{104}{26}=4$

The solution is ...

... B. (1, 4)