Question

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

A. (–1,3)

B. (1,4)

C. (–4,–5)

D. No unique solution

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

The solution is ...

... B. (1, 4)