Answer:
The answer is the 1st [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]
Step-by-step explanation:
Lets revise the Cramer's rule
- If the system of equation is ax + by = c and dx + ey = f
- A is the matrix represent this system of equation
- The first column has the coefficients of x, and
the second column has the coefficients of y
∴ A = [tex]\left[\begin{array}{cc}a&b\\d&e\end{array}\right][/tex]
- Ax means replace the column of x by the answers of the equation
∴ Ax = [tex]\left[\begin{array}{ccc}c&b\\f&e\end{array}\right][/tex]
- Ay means replace the column of y by the answers of the equation
∴ Ay = [tex]\left[\begin{array}{ccc}a&c\\d&f\end{array}\right][/tex]
- x = Dx/D, where Dx is the determinant of Ax and D is the determinant
of A
- The determinant of A = ae - bd
- The determinant of Ax = ce - bf
* Now lets solve the problem
∵ x + 3y = 16 and 3x + y = 8
∴ A = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right][/tex]
- Replace the column of x by the answer to get Ax
∴ Ax = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right][/tex]
∵ [tex]x=\frac{Dx}{D}[/tex]
∵ Dx = [tex]\left[\begin{array}{cc}16&3\\8&1\end{array}\right]=(16)(1)-(3)(8)=16-24=-8[/tex]
∵ D = [tex]\left[\begin{array}{cc}1&3\\3&1\end{array}\right]=(1)(1)-(3)(3)=1-9=-8[/tex]
∴ x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=\frac{-8}{-8}=1[/tex]
* x = [tex]\frac{\left[\begin{array}{cc}16&3\\8&1\end{array}\right]}{-8}=1[/tex]
