Exam 10: Systems of Equations and Inequalities

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { r r | r } 9 & - 5 & - 6 \\- 7 & - 2 & - 5\end{array} \right]$

Perform the matrix multiplication. -Let $A = \left[ \begin{array} { l } - 2 \\ 1 \\ - 1 \end{array} \right]$ and $B = \left[ \begin{array} { l l l } 1 & - 1 & 0 \end{array} \right]$ Find $\mathrm { AB } .$

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - $\left\{ \begin{aligned}- 3 x - y + 8 z & = 16 \\- 9 x + 6 z & = - 33 \\4 y + z & = 17\end{aligned} \right.$

Perform the indicated operation, whenever possible. - $\left[ \begin{array} { r r } - 1 & 0 \\6 & 2\end{array} \right] - \left[ \begin{array} { r r } - 1 & 6 \\3 & 1\end{array} \right]$

Solve the system. - $\left\{ \begin{array} { c } x + 5 y = 4 \\3 x + 15 y = 12\end{array} \right.$

Solve the problem. -A rectangular piece of tin has an area of 703 square inches. A square of 4 inches is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box is 1,276 cubic inches, what were the Original dimensions of the piece of tin?

Graph the system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. - $\left\{ \begin{array} { l } x \geq 0 \\y \geq 0 \\x + y \leq 3 \\x + y \geq 2\end{array} \right.$ A) unbounded; corner points $(3,0),(0,3)$ B) $\text { no solution }$ C) unbounded; corner points $( 0,0 ) , ( 0,2 ) , ( 2,0 )$ D) bounded; corner points $( 3,0 ) , ( 0,3 ) , ( 0,2 ) , ( 2,0 )$

Write the partial fraction decomposition of the rational expression. - $\frac { 13 x ^ { 2 } - x - 18 } { x ( x + 1 ) ( x - 1 ) }$

Solve the system of equations. - $\left\{ \begin{array} { l } x - y + 3 z = - 4 \\3 x + z = 0 \\- x + y - 3 z = 16\end{array} \right.$

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - x-y+2z+w=2 y+z=2 z-w=3

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 4 & 0 \\- 1 & - 1\end{array} \right]$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -5+3 =49 x+6y =3

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { c c | c } 9 & 7 & 17 \\7 & 18 & 5\end{array} \right]$

Perform the indicated matrix operations. -Let $B = \left[ \begin{array} { l l l l } - 1 & 1 & 6 & - 3 \end{array} \right]$ . Find $- 4 B$ .

Graph the inequality. - $-3 x-4 y \leq-12$ A) B) C) D)

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 2 & 5 \\- 5 & - 3\end{array} \right]$

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - 2=y+5 y=-10x+3

Use a graphing utility to solve the system of equations. Express the solution rounded to two decimal places. - $\left\{ \begin{array} { r } 3 x ^ { 3 } + y ^ { 2 } = 6 \\x ^ { 4 } y = 2\end{array} \right.$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 81 \\x ^ { 2 } - y ^ { 2 } = 81\end{array} \right.$

Graph the inequality. - $y \leq x ^ { 2 } + 5$ A) B) C) D)