Exam 7: Systems Of Equations and Inequalities

Use a graphing utility to solve the system of equations.Find the solution(s) accurate to two decimal places. $\left\{ \begin{aligned}y & = e ^ { x + 4 } \\x - y + 5 & = 0\end{aligned} \right.$

For a concert event, there are $30 reserved seat tickets and $20 general admission tickets.There are 2000 reserved seats available, and fire regulations limit the number of paid ticket holders to 3000.The promoter must take in at least $65,000 in ticket sales.Find and graph a system of inequalities describing the different numbers of tickets that can be sold.

Solve the system of linear equations by the method of elimination, find (x,y). $\left\{ \begin{array} { l } \frac { x + 23 } { 8 } + \frac { y + 10 } { 7 } = 3 \\x - 9 y = 20\end{array} \right.$

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants. $\frac { x - 3 } { 6 x ^ { 3 } + 24 x }$

Find the minimum value of the objective function and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 4x + 5y ​ Constraints: ​ X ≥ 0 ​3x - y ≤ 9 2x + 3y ≥ 6 X + 4y ≤ 16 ​​ ​

An animal shelter mixes two brands of dog food.Brand X costs $29 per bag and contains two units of nutritional element A, two units of element B, and two units of element C.Brand Y costs $22 per bag and contains one unit of nutritional element A, nine units of element B, and three units of element C.The minimum required amounts of nutrients A, B, and C are 12 units, 36 units, and 24 units, respectively.What is the optimal number of bags of each brand that should be mixed? What is the optimal cost?

Find the maximum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = x + 9y Constraints: X $\ge$ 0 Y $\ge$ 0 X + 4y $\le$ 20 X + y $\le$ 18 2x + 2y $\le$ 21

Find the dimensions of the rectangle meeting the specified condition. ​ The perimeter is 70 inches and the width is three-fourths the length. ​

Use back-substitution to solve the system of linear equations. $\left\{ \begin{array} { c c c } 4 x - 3 y - 2 z & = & 21 \\6 y - 5 z & = & 5 \\z & = & - 7\end{array} \right.$

Solve the system. $\left\{ \begin{array} { l } 12 x - 28 y = 12 \\- 6 x + 14 y = - 6\end{array} \right.$

Write the partial fraction decomposition of the rational expression. $\frac { 7 x ^ { 2 } - 3 x - 6 } { x ^ { 3 } - x }$

A small corporation borrowed $800,000 to expand its line of toys.Some of the money was borrowed at 8%, some at 9%, and some at 10%.How much was borrowed at each rate if the annual interest owed was $67,400 and the amount borrowed at 8% was five times the amount borrowed at 10%? ​

Solve the system, if possible. $\left\{ \begin{array} { l } 8 x + 5 y + 6 z = 22 \\4 x - 9 y + 2 z = 78 \\7 x - 7 y - 10 z = 57\end{array} \right.$

Write an inequality for the shaded region shown in the figure.

Write the partial fraction decomposition of the rational expression.Check your result algebraically. $\frac { 5 } { x ^ { 2 } - 5 x }$

Solve the system of linear equations using any method, find (x,y). $\left\{ \begin{array} { r } 9 x - 2 y = 1 \\- 3 x + 2 y = 7\end{array} \right.$

Solve the system of linear equations using any method, find (x,y). $\left\{ \begin{array} { l } 3 x + 8 y = 2 \\y = x - 5\end{array} \right.$

Solve the system by the method of substitution. $\left\{ \begin{aligned}x - y & = 4 \\7 x - 4 y & = 37\end{aligned} \right.$

Determine which ordered pair is a solution of the system. $\left\{ \begin{array} { l } - x + 9 y ^ { 2 } = 12 \\- 4 x + 9 y = 3\end{array} \right.$

Find the minimum value of the objective function and where it occurs, subject to the constraints: Objective function: Z = 5x + 6y Constraints: X $\ge$ 0 Y $\ge$ 0 X + 4y $\le$ 20 X + y $\le$ 18 2x + 2y $\le$ 21