Exam 41: Linear and Nonlinear Systems of Equations

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

Find the dimensions of the rectangle meeting the specified condition. ​ The perimeter is 36 meters and the length is 4 meters greater than the width. ​

Solve the system by the method of substitution.​ $\left\{ \begin{array} { l } 1.3 x + 0.6 y = 5.7 \\0.9 x - 0.2 y = 2.1\end{array} \right.$ ​

The sales of various types of lawn and garden tools vary according to the season.At a certain home improvement store,the monthly sales H of garden hoes (hoes sold per month)decline from July to October whereas the monthly sales of lawn rakes R (rakes sold per month)increase during this same interval.The sales of these two items during the calendar months July-October are modeled by the equations:​ H(t)=64-6t R(t)=17t-143 ​ where t is the month (t = 7 corresponds to July).In which month does the number of rakes sold equal the number of hoes sold? ​

Solve the system by substitution,if possible.​ $\left\{ \begin{array} { l } - 6 x + 7 y = 50 \\12 x + 14 y = 124\end{array} \right.$ ​

Select the ordered pair that is a solution of the system of equations.​ $\left\{ \begin{array} { l } 2 x - y = 3 \\8 x + y = - 18\end{array} \right.$

Solve the system graphically.​ $\left\{ \begin{aligned}x - y & = 1 \\6 x - 3 y & = 24\end{aligned} \right.$ ​ ​

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. )​ $C = 6.5 \sqrt { x } + 9,674 , R = 3.2 x$ ​

Solve the system by the method of substitution.​ $\left\{ \begin{array} { l } y = x ^ { 3 } - 6 x ^ { 2 } + 4 \\y = x ^ { 2 } - 10 x + 4\end{array} \right.$ ​

Solve the system graphically.​ $\left\{ \begin{aligned}x - 3 y & = - 7 \\5 x + 3 y & = - 8\end{aligned} \right.$ ​

Solve the system by the method of substitution.Check your solution(s)graphically.​ $\left\{ \begin{array} { r } 2 x + y = 9 \\- x + y = 0\end{array} \right.$ ​

Find the dimensions of the rectangle meeting the specified conditions. The perimeter is 48 meters and the length is 2 meters more than the width.

Solve the system by the method of substitution.​ $\left\{ \begin{array} { l } 2 x - y + 2 = 0 \\4 x + y - 5 = 0\end{array} \right.$ ​ ​

Solve the system by the method of substitution.Check your solution(s)graphically.​ $\left\{ \begin{array} { l } x - 2 y = - 9 \\x + 3 y = 1\end{array} \right.$ ​ ​

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

Solve the system by substitution,if possible.​ $\left\{ \begin{array} { l } y = 7 x - 21 \\9 x - y = 29\end{array} \right.$ ​

Solve the system by the method of substitution.​ $\left\{ \begin{array} { l } 0.5 x + 3.2 y = 5.3 \\0.3 x - 1.4 y = - 1.8\end{array} \right.$ ​

Solve the system by the method of substitution.Check your solution(s)graphically.​ $\left\{ \begin{array} { r } x ^ { 2 } + 2 y = 0 \\x ^ { 2 } - 6 x - y = 0\end{array} \right.$ ​ ​

Find the dimensions of the rectangle meeting the specified condition. ​ The perimeter is 30.6 millimeters and the length is 2.4 times the width. ​

Solve the system by the method of substitution. ​​ $\left\{ \begin{array} { r } 9 x - 4 y - 2 = 0 \\x + 9 y - 4 = 0\end{array} \right.$ ​