Exam 10: Systems of Equations and Inequalities

Choose the one alternative that best completes the statement or answers the question. Find the value of the determinant. - $\left| \begin{array} { r r } 3 & - 1 \\- 1 & 2\end{array} \right|$

Graph the inequality. - $x^{2}+y^{2} \leq 1$

Choose the one alternative that best completes the statement or answers the question. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

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

Choose the one alternative that best completes the statement or answers the question. Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[ \begin{array} { r r r r } 1 & - 9 & 0 & 0 \\0 & 1 & - 7 & 0 \\0 & 0 & 1 & 1 \\0 & 0 & 0 & 1\end{array} \right]$

Write a system of linear inequalities that has the given graph. -

Graph the system of linear inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. - $\left\{ \begin{array} { l } x \geq 0 \\y \geq 0 \\x + y \leq 3 \\x + y \geq 2\end{array} \right.$

Choose the one alternative that best completes the statement or answers the question. Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } 4 x - 7 y = 5 \\2 x + 5 y = - 3\end{array} \right.$

Use the properties of determinants to find the value of the second determinant, given the value of the first. - $\left| \begin{array} { r r r } x & y & z \\ u & v & w \\ 1 & - 3 & - 3 \end{array} \right| = 66 \left| \begin{array} { r r r } x & z \\ u & v & w \\ - 2 & 6 & 6 \end{array} \right| = ?$

Solve the problem. -A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 5 soft drinks for $40.29. The second group bought 6 slices of pizza and 7 soft drinks for $ 35)71. How much does one slice of pizza cost?

Solve the system using the inverse method. - $\left\{ \begin{array} { l } x + 2 y + 3 z = 10 \\x + y + z = 2 \\x - 2 z = - 1\end{array} \right.$

Perform the indicated matrix operations. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 3 & 3 \\ 0 & 2 \end{array} \right]$ . Find $3 \mathrm {~A}$ .

2x + 3y ≥6 - y-x\leq5 x+y\geq3 y-3x\geq-1

Use the properties of determinants to find the value of the second determinant, given the value of the first. - $\left| \begin{array} { c c c } x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{array} \right| = - 64 \left| \begin{array} { c c c } x - 2 & y - 4 & z - 6 \\ - 2 u - 1 & - 2 v - 2 & - 2 w - 3 \\ 1 & 2 & 3 \end{array} \right| = ?$

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - $\left\{ \begin{array} { l } 5 x + 6 y = 20 \\2 x + 8 y = 36\end{array} \right.$

Choose the one alternative that best completes the statement or answers the question. -The perimeter of a rectangle is 22 inches and its area is 28 square inches. What are its dimensions?

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -The Jillson's have up to $75,000 to invest. They decide that they want to have at least $25,000 invested in stable bonds yielding 6% and that no more than $45,000 should be invested in more volatile bonds yielding 12%. How much should they invest in each type of bond to maximize income if the amount in the more volatile bond should not exceed the amount in the more stable bond? What is the maximum income?

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 61 \\x ^ { 2 } - y ^ { 2 } = 11\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x + 5 } { x ^ { 3 } - 2 x ^ { 2 } + x }$

Solve the system of equations using elimination. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 64 \\\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1\end{array} \right.$