Exam 41: Linear and Nonlinear Systems of Equations

A small fast-food restaurant invests $5,951 to produce a new food item that will sell for $3.81.Each unit can be produced for $2.50.How many items must be sold to break even? ​

Solve the system graphically or algebraically.Find the solution(s)accurate to three decimal places.​ $\left\{ \begin{array} { r } y - e ^ { - x } = 3 \\y - \ln x = 5\end{array} \right.$ ​

Solve the system graphically.​ $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 85 \\( x - 5 ) ^ { 2 } + y ^ { 2 } & = 50\end{aligned} \right.$ ​ ​

Solve the system by substitution,if possible.​ $\left\{ \begin{array} { l } - 8 x + 7 y = - 11 \\16 x + 14 y = 106\end{array} \right.$ ​

Solve the system graphically.​ $\left\{ \begin{aligned}x + y & = 0 \\3 x - 2 y & = 10\end{aligned} \right.$ ​

Solve the system by the method of substitution.​ $\left\{ \begin{aligned}- \frac { 2 } { 3 } x + y & = 8 \\2 x - 3 y & = 20\end{aligned} \right.$ ​

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

​Solve the system by the method of substitution. ​​ $\left\{ \begin{array} { l } \frac { 1 } { 10 } x + \frac { 3 } { 10 } y = 1 \\\\- \frac { 1 } { 5 } x + \frac { 2 } { 5 } y = 1\end{array} \right.$ ​

Find the dimensions of the rectangle meeting the specified condition. ​ The perimeter is 352 centimeters and the length is 4 centimeters greater than the width. ​

Solve the system by substitution,if possible.​ $\left\{ \begin{array} { l } 4 x + 3 y = 23 \\8 x + 6 y = 24\end{array} \right.$ ​

Use a graphing utility to solve the system of equations.Find the solution accurate to two decimal places.​ $\left\{ \begin{array} { l } y = 2 e ^ { - x } \\y = \ln ( x - 2 ) + 1\end{array} \right.$ ​

Select the ordered pair that is a solution of the system of equations.​ $\left\{ \begin{aligned}y & = - 6 e ^ { x } \\- 7 x - y & = 6\end{aligned} \right.$ ​

Determine which ordered pair is a solution of the system.​ $\left\{ \begin{array} { l } - 8 x + 7 y = - 10 \\- 9 x + 4 y = 12\end{array} \right.$ ​

Solve the system by the method of substitution.Check your solution(s)graphically.​ $\left\{ \begin{aligned}x - y & = - 3 \\x ^ { 2 } - y & = 3\end{aligned} \right.$ ​​ ​

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

Solve the system graphically.​ $\left\{ \begin{array} { r } - x + 2 y = 3 \\x - y = 2\end{array} \right.$ ​ ​

Solve the system by the method of substitution.​ $\left\{ \begin{aligned}6 x + 5 y & = - 6 \\- x - \frac { 5 } { 6 } y & = - 3\end{aligned} \right.$ ​

The total weekly sales for a newly released portable media player (PMP)increased each week.At the same time,the total weekly sales for another newly released PMP decreased each week.Models that approximate the total weekly sales S (in thousands of units)for each PMP are​ $\left\{ \begin{array} { l l } S = 10 x + 70 & \text { PMP1 } \\S = - 10 x + 210 & \text { PMP2 }\end{array} \right.$ ​ where x represents the number of weeks each PMP was in stores,with x = 0 corresponding to the PMP sales on the day each PMP was first released in stores.After how many weeks will the sales for the two PMPs be equal? ​

Find the sales necessary to break even (R - C = 0)for the cost C of producing x units and the revenue R obtained by selling x units.(Round to the nearest whole unit. )​ $C = 6.7 \sqrt { x } + 3000 , R = 8.1 x$ ​

What are the dimensions of a rectangular tract of land if its perimeter is 50 kilometers and its area is 150 square kilometers? ​