Exam 41: Linear and Nonlinear Systems of Equations

Select the ordered pair that is a solution of the system of equations.​ $\left\{ \begin{array} { c } 2 x ^ { 2 } + y = - 11 \\- x - y = 12\end{array} \right.$ ​

Solve the system by the method of substitution.​ $\left\{ \begin{array} { l } y = - 4 x \\y = x ^ { 3 } + x ^ { 2 } - x\end{array} \right.$ ​

Solve the system graphically.​ $\left\{ \begin{array} { l } x - y = 0 \\5 x - 2 y = 9\end{array} \right.$

Find the dimensions of the rectangle meeting the specified condition. ​ The perimeter is 528 feet and the length is $4 \frac { 1 } { 2 }$ times the width. ​

​Solve the system of equations by graphing.​ $\left\{ \begin{array} { l } 2 x + 3 y = 28 \\6 x + 5 y = 60\end{array} \right.$ ​ ​

Solve the system of equations by graphing. ​​ $\left\{ \begin{aligned}x + y & = 0 \\6 x - 7 y & = 13\end{aligned} \right.$ ​

Solve the system by the method of substitution.​ $\left\{ \begin{aligned}x - y & = - 8 \\x ^ { 2 } - y & = - 21\end{aligned} \right.$ ​

Solve the system graphically.​ $\left\{ \begin{aligned}6 x + 8 y & = 48 \\x - 8 y & = - 20\end{aligned} \right.$ ​ ​

Solve the system by the method of substitution.Check your solution(s)graphically.​ $\left\{ \begin{array} { r } 7 x + y = 3 \\x ^ { 3 } - 3 + y = 0\end{array} \right.$ ​ ​

A small software company invests $24,425 to produce a software package that will sell for $70.Each unit can be produced for $45.84.How many units must be sold to break even? ​

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

The weekly rentals for a newly released DVD of an animated film at a local video store decreased each week.At the same time,the weekly rentals for a newly released DVD of a horror film increased each week.Models that approximate the weekly rentals R for each DVD are​ $\left\{ \begin{array} { l l } R = 380 - 24 x & \text { Animated film } \\R = 28 + 20 x & \text { Horror film }\end{array} \right.$ ​ where x represents the number of weeks each DVD was in the store,with x = 1 corresponding to the first week.After how many weeks will the rentals for the two movies be equal? ​

Find the sales necessary to break even (R = C)for the cost C of producing x units and the revenue R obtained by selling x units.(Round to the nearest whole unit. ) ​ C = 8630x + 264,000,R = 9950x ​

Solve the system of equations by graphing.​ $\left\{ \begin{array} { l } 4 x - 9 y = - 60 \\2 x + 9 y = 78\end{array} \right.$ ​

Solve the system by the method of substitution.​ $\left\{ \begin{aligned}\frac { 1 } { 5 } x + \frac { 1 } { 2 } y & = 8 \\x + y & = 21\end{aligned} \right.$ ​

Select the ordered pair that is a solution of the system of equations.​ $\left\{ \begin{aligned}- \log x + 3 & = 2 \\\frac { 1 } { 9 } x + y & = \frac { 28 } { 9 }\end{aligned} \right.$ ​

What are the dimensions of an isosceles right triangle with a four-inch hypotenuse and an area of 4 square inches? ​

Solve the system by the method of substitution.​ $\left\{ \begin{aligned}x - y & = - 22 \\x ^ { 2 } - y & = - 2\end{aligned} \right.$ ​