Exam 8: Systems of Equations and Inequalities

Use Mathematical Models Involving Linear Inequalities -A man is planting a section of garden with tomatoes and cucumbers. The available area of the section is 110 square feet. He wants the area planted with tomatoes to be more than 40% of the area planted with cucumbers. Write a system of inequalities to describe the situation. Let x = amount to be planted in tomatoes and y = amount to be planted in cucumbers.

Linear Programming 1 Write an Objective Function Describing a Quantity That Must be Maximized or Minimized -A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $\$ 0.25$ and an ounce of potatoes for $\$ 0.04$ . Let $x =$ the number of ounces of chicken and $y =$ the number of ounces of potatoes purchased per patient. Write the objective function that describes the total cost per patient per meal.

Graph the inequality. - $y \geq x - 2$

Use Linear Programming to Solve Problems -Objective Function z=5x+7y x\geq0 0\leqy\leq5 2x+3y\geq12 2x+3y\leq20 $\text { Constraints } \quad x \geq 0$

Systems of Nonlinear Equations in Two Variables 1 Recognize Systems of Nonlinear Equations in Two Variables - $\left\{ \begin{array} { l } x ^ { 3 } + 8 x = y \\x + 8 y = 3\end{array} \right.$

Solve Problems Using Systems of Linear Equations -A rectangular lot whose perimeter is 400 feet is fenced along three sides. An expensive fencing along the lot's length costs $\$ 21$ per foot, and an inexpensive fencing along the two side widths costs only $\$ 10$ per foot. The total cost of the fencing along the three sides comes to $\$ 4140$ . What are the lot's dimensions?

Solve Systems of Linear Equations in Three Variables - x+4y+5z =26 2y+3z =11 z =1

Use Linear Programming to Solve Problems - Objective Function z=6x+7y Constraints x\geq0 y\geq0 2x+3y\leq12 2x+y\leq8

Solve Nonlinear Systems By Substitution - +=25 x+y=-7

Solve Linear Systems by Addition - 6x+8y=8 6x-2y=-2

Graph the solution set of the system of inequalities or indicate that the system has no solution. - x+2y\geq2 x-y\leq0

Write the word or phrase that best completes each statement or answers the question. -The Fiedler family has up to $130,000 to invest. They decide that they want to have at least $40,000 invested in stable bonds yielding 5.5% and that no more than $60,000 should be invested in more volatile bonds yielding 11%. How much should they invest in each type of bond to maximize income if the amount in the stable bond should not exceed the amount in the more volatile bond? What is the maximum income?

Solve Linear Systems by Addition - 6y=63-7x 2x=78-6y

Determine whether the given ordered pair is a solution of the system. - (3,3) x+y=0 x-y=-6

Use Mathematical Models Involving Linear Inequalities -A bakery plans to market a mixed assortment of its two most popular cookies, Chocolate Chip and Toffee Chunk. The marketing analyst proposes that the new assortment be constrained by the inequality 3C + 4T ≤ 31, where C is the number of Chocolate Chip cookies and T is the number of Toffee Chunk cookies. The sales analyst suggests that the assortment should be constrained by the inequality 5C + 2T ≤ 33. The number of each type of cookie cannot be negative, so C ≥ 0 and T ≥ 0. Graph the region satisfying all the requirements for the assortment using C as the horizontal axis and T as the vertical axis. Does the combination of 7 Chocolate Chip cookies and 2 Toffee Chunk cookies satisfy all of the requirements?

Solve Nonlinear Systems By Addition - 7+=49 7-=49

Solve Linear Systems by Addition - 3x+7y=46 3x+2y=56

Solve Problems Using Systems of Linear Equations -As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The weekly supply and demand models for a certain type of television are as follows: Demand: $\mathrm { N } = - 3 \mathrm { p } + 780$ Supply: $\quad N = 2.5 p$ where $\mathrm { p }$ is the price in dollars per television. Find the price at which supply and demand are equal. At this price, how many televisions can be supplied and sold each week?

Solve Problems Using Systems of Linear Equations -Two cars leave a city and head in the same direction. After 7 hours, the faster car is 63 miles ahead of the slower car. The slower car has traveled 336 miles. Find the speeds of the two cars.

Solve Problems Using Systems of Linear Equations -In 1985, in the town of Appleby, $21.2 \%$ of Hispanics were overweight, increasing by an average of $0.42 \%$ per year. In 1985, in the town of Appleby, $0.17 \%$ of whites were overweight, increasing by an average of $31.0 \%$ per year. Write a function that models the percentage, $y$ , of Hispanics who are overweight x years after 1985. Write a function that models the percentage, $y$ , of whites who are overweight x years after $1985 .$