Exam 10: Systems of Equations and Inequalities

Solve the problem. -An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

Graph the system of inequalities. - y-x\leq5 x+y\geq3 y-3x\geq-1 A) B) C) D)

Solve the problem using matrices. -A company manufactures three types of wooden chairs: the Kitui, the Goa, and the Santa Fe. To make a Kitui chair requires 1 hour of cutting time, 1.5 hours of assembly time, and 1 hour of finishing time. A Goa chair requires 1.5 hours of cutting time, 2.5 hours of assembly time and 2 hours of finishing time. A Santa Fe chair requires 1.5 hours of cutting time, 3 hours of assembly time, and 3 hours of finishing time. If 41 hours of cutting time, 70 hours of assembly time, and 58 hours of finishing time were used one week, how many of each type of chair were produced?

Solve the system using the inverse method. - $\left\{ \begin{array} { r } 2 x + 4 y - 5 z = - 8 \\x + 5 y + 2 z = - 1 \\3 x + 3 y + 3 z = 15\end{array} \right.$

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?

Solve the system of equations by using substitution. - $\left\{ \begin{array} { r } 5 x - 2 y = - 1 \\x + 4 y = 35\end{array} \right.$

Graph the system of inequalities. - $\left\{\begin{array}{c}-x+2 y \leq-6 \\3 x+2 y>-18\end{array}\right.$ A) B) C) D)

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } y = 6 x ^ { 2 } - 5 x \\y = 2 x + 3\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$

Solve the system using the inverse method. - $\left\{ \begin{aligned}x + 3 y & = - 8 \\21 x + 6 y & = 3\end{aligned} \right.$

Solve the system using the inverse method. - $\left\{ \begin{array} { r r } x + 2 y + 3 z = & 11 \\x + y + z = & 3 \\2 x + 2 y + z = & 10\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 169 \\x + y = 17\end{array} \right.$

Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } - 2 x + 4 y = - 12 \\- 2 x + 5 y = - 11\end{array} \right.$

Use Cramer's rule to solve the linear system. - $\left\{ \begin{array} { l } 4 x - 7 y = 5 \\2 x + 5 y = - 3\end{array} \right.$ A) $x = - \frac { 2 } { 17 } , y = \frac { 11 } { 17 }$ B) $x = \frac { 23 } { 3 } , y = - \frac { 11 } { 3 }$ C) $x = \frac { 2 } { 17 } , y = - \frac { 11 } { 17 }$ D) $x = \frac { 2 } { 3 } , y = \frac { 1 } { 3 }$

Graph the inequality. - $x^{2}+y^{2}>16$ A) B) C) D)

Solve the system. - $\left\{ \begin{array} { l } 4 x - 7 y = 8 \\4 x - 7 y = - 5\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{array} { c } x + y + z = - 5 \\x - y + 5 z = 3 \\4 x + y + z = - 17\end{array} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { r } x y = 20 \\x + y = 9\end{array} \right.$

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?

Perform the indicated operation, whenever possible. -Let $\mathrm { A } = \left[ \begin{array} { r r r } - 4 & 6 & 7 \\ 3 & - 5 & 12 \\ 7 & - 11 & 14 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { r r r } 6 & 10 & - 4 \\ - 5 & 6 & - 8 \\ 3 & 11 & 7 \end{array} \right]$ . Find $\mathrm { A } - \mathrm { B }$