Exam 7: Systems Of Equations and Inequalities

Solve the system of linear equations. $\left\{ \begin{array} { c l } x + y + z + w & = - 1 \\- 2 x + y + 3 z - w & = 6 \\2 x + 2 z - 2 w & = - 18 \\2 x + 4 y - 4 z + w & = 5\end{array} \right.$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 4 b + 4 m = \frac { 156 } { 35 } \\4 b + 11 m = \frac { 471 } { 35 }\end{array} \right.$

For the given supply and demand equations, find the consumer surplus. Demand Supply p=100-0.00006x p=80+0.00002x

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

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

An airplane flying into a headwind travels 1128.00 miles in 4 hours and 42 minutes.On the return flight, the distance is traveled in 4 hours.Find the airspeed of the plane and the speed of the wind, assuming that both remain constant. ​

Find the minimum value of the objective function and where it occurs, subject to the indicated constraints. ​ Objective function: ​ Z = 4x + 16y ​ Constraints: ​ X ≥ 0 Y ≥ 0 2x + y ≤ 12​ ​

Solve the system of linear equations by the method of elimination.Use the graph to check your solution. $\left\{ \begin{array} { l } 9 x + 4 y = 4 \\18 x + 8 y = 16\end{array} \right.$

Select the correct graph of the inequality. $y < - 1.8 x + 1.1$

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

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

Write the partial fraction decomposition of the rational expression. $\frac { 3 } { x ^ { 2 } + 5 x + 4 }$

Select the correct graph of the inequality. $y > - 4$

Solve the system of linear equations by the method of elimination.Find (x,y) and check your solution algebraically. $\left\{ \begin{array} { l } 0.2 x - 0.5 y = - 27.1 \\0.3 x + 0.4 y = 70.9\end{array} \right.$

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

Find the consumer surplus and producer surplus. Demand $p = 600 - 0.0002 x$ Supply $p = 450 + 0.0001 x$

Determine which one of the ordered pairs below is a solution of the system of linear inequalities. $\left\{ \begin{array} { c } x > - 3 \\y > - 1 \\y \leq 4 - \frac { 2 x } { 3 }\end{array} \right.$

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

A dietitian is asked to design a special dietary supplement using two different foods.Each ounce of food X contains 20 units of calcium, 15 units of iron, and 10 units of vitamin B.Each ounce of food Y contains 10 units of calcium, 10 units of iron, and 20 units of vitamin B.The minimum daily requirements of the diet are 350 units of calcium, 300 units of iron, and 400 units of vitamin B.Write a system of inequalities describing the different amounts of food X and food Y that can be used.