Exam 8: Systems of Equations and Inequalities

Write the word or phrase that best completes each statement or answers the question. -A coffee store has available 75 pounds of A grade coffee and 120 pounds of B grade coffee. These will be blended into 1 pound packages as follows: an economy blend that contains 4 ounces of A grade coffee and 12 ounces of B grade coffee and a superior blend that contains 8 ounces of A grade coffee and 8 ounces of B grade coffee. Using $x$ to denote the number of packages of the economy blend and $y$ to denote the number of packages of the superior blend, write a system of linear inequalities that describes the possible number of packages of each blend. Graph the system of inequalities.

Systems of Nonlinear Equations in Two Variables 1 Recognize Systems of Nonlinear Equations in Two Variables - $\left\{ \begin{array} { l } x ^ { 2 } = 7 y + 2 \\4 x - y = 8\end{array} \right.$

Use Inequalities to Describe Limitations in a Situation -A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $\$ 0.25$ and an ounce of potatoes for $\$ 0.02$ . The dietician is bound by the following constraints. - Each ounce of chicken contains 13 grams of protein and 24 grams of carbohydrates. - Each ounce of potatoes contains 5 grams of protein and 35 grams of carbohydrates. - The minimum daily requirements for the patients under the dietitian's care are 45 grams of protein and 58 grams of carbohydrates. Let $x =$ the number of ounces of chicken and $y =$ the number of ounces of potatoes purchased per patient. Write a system of inequalities that describes these constraints.

Graph the inequality. - $5 x+y \leq-5$

Systems of Linear Equations in Three Variables 1 Verify the Solution of a System of Linear Equations in Three Variables - (5,2,-2) x+3y+4z =24 5y+5z =35 z =5

Use Linear Programming to Solve Problems -Objective Function: $z = - 5 x - y$ Find maximum.

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - 4x+y=3 2y=6-8x

Graph the solution set of the system of inequalities or indicate that the system has no solution. - -2x+y<2 -2x+y>-1

Graph the inequality. - $x - y < - 6$

Write the partial fraction decomposition of the rational expression. - $\frac { 5 x + 6 } { ( x - 6 ) ^ { 2 } }$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - x+2y\geq-2 x>-4 y\leq6

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - 9x-2y=7 -27x+6y=-14

Solve Problems Using Systems of Linear Equations -Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 9 times as many dimes as nickels, and the value of the dimes is $\$ 10.20$ more than the value of the nickels. How many nickels and dimes does Jamil have?

Solve Linear Systems by Substitution - y=2x-6 y=7x-5

Solve Problems Using Systems of Linear Equations -You invested $\$ 13,200$ and started a business selling vases. Supplies cost $\$ 20$ per vase and you are selling each vase for $\$ 31$ . Let $x$ represent the number of vases produced and sold and write the cost function, $C$ , and revenue function, $R$ .

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y<-x+5 y>2x-3

Graph the solution set of the system of inequalities or indicate that the system has no solution. - +\leq81 +\geq16

Solve Nonlinear Systems By Addition - ++6x+2y-15=0 -+6x-2y-17=0

Graph a Nonlinear Inequality in Two Variables - $y \leq x^{2}-3$

Solve Problems Using Systems in Three Variables -A store sells tents, sleeping bags, and camp stools. A customer buys a tent, 5 sleeping bags, and 2 camp stools for $\$ 360$ . The price of the tent is 9 times the cost of a camp stool. The cost of a sleeping bag is $\$ 40$ more than the cost of a camp stool. Find the cost of each item.