Exam 10: Systems of Equations and Inequalities

Find the value(s) of the function, subject to the system of inequalities. -Find the maximum and minimum of $z = 19 x + 7 y$ subject to $x \geq 0 , y \geq 0,2 x + 3 y \geq 6 , x \leq 10$ , $y \leq 5$ .

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. - $\left\{ \begin{array} { l } x - 4 y = - 10 \\2 x - 8 y = - 17\end{array} \right.$

Write the word or phrase that best completes each statement or answers the question. - $\frac { x ^ { 2 } - 56 } { x ^ { 4 } + 5 x ^ { 2 } - 36 }$

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

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

Solve the system of equations. - $\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } = 4 \\x + y = 2\end{array} \right.$

Solve the system of equations. - $\left\{ \begin{aligned}x + y + z & = 0 \\x - y + 4 z & = - 11 \\3 x + 3 y + 3 z & = 4\end{aligned} \right.$

Find the value of the determinant. - $\left| \begin{array} { r r r } 2 & 3 & 4 \\- 1 & - 4 & - 2 \\- 2 & - 4 & - 1\end{array} \right|$

Choose the one alternative that best completes the statement or answers the question. -A right triangle has an area of 33 square inches. The square of the hypotenuse is 157. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Choose the one alternative that best completes the statement or answers the question. -The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 Man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the Company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?

Choose the one alternative that best completes the statement or answers the question. - $\frac { 14 x + 1 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 0 & - 3 \\- 3 & - 6\end{array} \right]$

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. - -5+3 =49 x+6y =3