91Ó°ÊÓ

Solve each system by substitution or addition, whichever is easier. $$ \begin{aligned} &3 x-2 y=2\\\ &x=\frac{2}{9} y \end{aligned} $$

Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent. $$\begin{aligned}&y=\frac{5}{7} x\\\&x=-\frac{2}{3} y\end{aligned}$$

Evaluate the determinant of each \(3 \times 3\) matrix using expansion by minors about the row or column of your choice. \(\left[\begin{array}{rrr}-2 & -3 & 0 \\ 4 & -1 & 0 \\ 0 & 3 & 5\end{array}\right]\)

Solve each system by substitution or addition, whichever is easier. \(y=3 x+1\) \(x=\frac{1}{3} y+5\)

Evaluate the determinant of each \(3 \times 3\) matrix using expansion by minors about the row or column of your choice. \(\left[\begin{array}{rrr}-2 & 6 & 3 \\ 0 & 4 & 0 \\ -1 & -4 & 5\end{array}\right]\)

Solve each system using the Gauss-Jordan elimination method. $$ \begin{aligned} -x \quad \quad &+z=-2 \\ 2 x-y &\quad\quad=5 \\ &y+3 z =9 \end{aligned} $$

Discussion Make up a system of three linear equations in three variables for which the solution set is \(\\{(0,0,0)\\} .\) A system with this solution set is called a homogeneous system. Why do you think it is given that name?

Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent. $$\begin{aligned}&7 y=9 x\\\&-3 x=4 y\end{aligned}$$

Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent. $$\begin{aligned}&3(y-1)=2(x-3)\\\&3 y-2 x=-3\end{aligned}$$

Solve each system using the Gauss-Jordan elimination method. $$ \begin{aligned} x-5 y &=11 \\ -2 x+10 y &=-22 \end{aligned} $$