Question

Use the Cramer’s Rule to solve each system.4. 6x+y=-28 -2x-2y=6

Answer 1

Given:

$\begin{gathered} 6x+y=-28...........(1) \\ -2x-2y=6............(2) \end{gathered}$

To find:

The solution.

Explanation:

Using the Cramer's rule,

$\begin{gathered} A=\begin{bmatrix}{6} & 1 \\ {-2} & {-2}\end{bmatrix} \\ |A|=6(-2)-1(-2) \\ =-12+2 \\ |A|=-10 \end{gathered}$$\begin{gathered} A_x=\begin{bmatrix}{-28} & {1} \\ {6} & {-2}\end{bmatrix} \\ |A_x|=(-28)(-2)-(1)(6) \\ =56-6 \\ =50 \end{gathered}$$\begin{gathered} A_y=\begin{bmatrix}{6} & {-28} \\ {-2} & {6}\end{bmatrix} \\ |A_y|=(6)(6)-(-28)(-2) \\ =36-56 \\ |A_y|=-20 \end{gathered}$

Let us find the value of x and y.

$\begin{gathered} x=\frac{|A_x|}{|A|}=\frac{50}{-10}=-5 \\ y=\frac{|A_y|}{|A|}=\frac{-20}{-10}=2 \end{gathered}$

Therefore, the solution is (-5, 2).

Final answer:

The value of x is -5 and the value of y is 2.

The solution is (-5, 2).