Solving Systems of Equations in Three Variables — Unit test Answers

Which system is equivalent to ?

Given that the solution set to a system of three linear equations is a line, which of the following is true about the system?

The constraints of a problem are listed below. What are the vertices of the feasible region?

An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?

Solve the system of equations.a.c.b.d.

A small organic food store makes two types of fruit smoothies: tropical and sport. Each tropical smoothie uses 9 oz of orange juice and 6 oz of milk. Each sport smoothie uses 3 oz of orange juice and 3 oz of milk. The store buys the orange juice in a 210-oz container and milk in a 150-oz container. The store sells the tropical smoothies for $4 and sells the sport smoothie for $3. What is the maximum in smoothie sales the store can make from 1 container each of orange juice and milk?

A group of children, adults, and senior citizens attended three different art exhibits that have different ticket prices for each age group. Let c represent the number of children, a represent the number of adults, and s represent the number of senior citizens. The system represents the cost of each type of ticket and the total cost of the tickets for all three exhibits. What are the numbers of children, adults, and seniors citizens that attended these three exhibits?

Which graph shows the solution to the following system of inequalities?

Michael is paid $9 per hour to work at the movie theater and $7 per hour when he helps his aunt at her bakery. Michael cannot work more than 32 hours in a week, but he wishes to earn at least $251 each week. Which weekly work schedule is within Michael’s constraints?

Which region represents the solution to the given system of inequalities?

What is one of the solutions to the following system?

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?

In their last basketball game, Becky scored twice as many points as Min. Together, they scored 42 points. How many points did Becky score?

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Which statement must be true?

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?

The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?

What is the solution to the following system?

Which equation can pair with x – y = –2 to create a consistent and dependent system?