Exam 10: Systems of Equations and Inequalities

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - $\left\{ \begin{array} { r } - 2 x - 8 y = - 8 \\4 x + 16 y = 3\end{array} \right.$

Graph the inequality. - $2 x+3 y \leq 6$

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$

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

Find the inverse of the matrix. - $\left[ \begin{array} { l l l } 1 & 3 & 2 \\1 & 3 & 3 \\2 & 7 & 8\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=9 x-9y=10

Solve the problem. -A retired couple has $170,000 to invest to obtain annual income. They want some of it invested in safe Certificates of Deposit yielding 5%. The rest they want to invest in AA bonds yielding 11% per year. How much Should they invest in each to realize exactly $16,300 per year?

Choose the one alternative that best completes the statement or answers the question. -(a) $R _ { 2 } = - 4 r _ { 1 } + r _ { 2 }$ (b) $R _ { 3 } = 4 r _ { 1 } + r _ { 3 }$ (c) $R _ { 3 } = 3 r _ { 2 } + r _ { 3 }$ $\left[ \begin{array} { r r r | r } 1 & - 3 & - 5 & 2 \\ 4 & - 5 & 2 & 5 \\ - 4 & - 5 & 4 & 6 \end{array} \right]$

Write the augmented matrix for the system. - $\left\{ \begin{aligned}8 x - 2 z & = 60 \\9 y + 7 z & = 33 \\2 x - 2 y + 9 z & = 74\end{aligned} \right.$

Tell whether the given rational expression is proper or improper. - $\frac { x ^ { 2 } - 9 x + 20 } { \left( x ^ { 2 } - 11 x + 30 \right) ( x + 5 ) }$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } y = x ^ { 2 } - 12 x + \\x + y = 18\end{array} \right.$

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

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. - -3+8=1 9x+9y=1

Graph the inequality. - $-2 x-4 y \leq 8$

Perform the matrix multiplication. -Let $A = \left[ \begin{array} { r r r } 0 & - 3 & 1 \\ 5 & - 1 & 0 \end{array} \right]$ and $B = \left[ \begin{array} { r r } 1 & 2 \\ 0 & 1 \\ 1 & - 1 \end{array} \right]$ . Find $A B$ .

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

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. - + =49 -6x-4y =7

Solve the system of equations. - $\left\{ \begin{aligned}2 x - y + 5 z & = - 7 \\x + y - 2 z & = - 2 \\x - y + 4 z & = 8\end{aligned} \right.$

Graph the region indicated by graphing the system of inequalities. Label all points of intersection. - $\left\{\begin{array}{l}y \geq x^{2}-8 \\y \leq-x^{2}\end{array}\right.$

2x + 3y ≥6 - $x ^ { 2 } + y ^ { 2 } \leq 100$ $6 x + 7 y \leq 42$