Learn Before
Solving by Graphing
Solve the system by graphing.
Graph . The boundary line is , which has intercepts and . Because the inequality uses (strict), draw a dashed line. Test : gives , which is true. So shade the side that contains .
Graph on the same grid. The boundary line is , a horizontal line passing through . Because the inequality uses (strict), draw a dashed line. Test : is true. So shade the side that contains .
Identify the solution. The point lies in the overlapping region and has already been verified as a solution of each inequality. The point where the two boundary lines intersect is not included in the solution because both boundary lines are dashed. The solution is the region where both shadings overlap — the darker-shaded area.
0
1
Tags
OpenStax
Elementary Algebra @ OpenStax
Ch.5 Systems of Linear Equations - Elementary Algebra @ OpenStax
Algebra
Math
Prealgebra
Related
Solving a System of Linear Inequalities by Graphing
Solving by Graphing
Solving by Graphing
Solving by Graphing
A System of Linear Inequalities with No Solution
A logistics coordinator is using a system of linear inequalities to determine the feasible number of shipments for two different routes. For a specific combination of shipments to be a valid solution for this system, it must satisfy:
A logistics manager is using a system of linear inequalities to represent fuel and time constraints for a delivery route. If a proposed schedule, represented as an ordered pair, satisfies the fuel inequality but does not satisfy the time inequality, that schedule is still considered a solution to the system.
In a warehouse management system, a set of linear inequalities is used to define the limits for storage space and weight capacity. For a specific inventory plan to be a valid solution, it must satisfy ____ of the inequalities in the system.
In the context of business constraint analysis, match each term related to a system of linear inequalities with its correct definition or graphical description.
Defining Solutions for Multi-Constraint Systems
A production manager is using a system of linear inequalities to find the 'feasible region' for manufacturing two different products, based on available machine time (x) and raw materials (y). Arrange the following steps in the correct order to graphically identify the solution set for this system.
Staffing Optimization and Budgetary Constraints
Defining Solutions in Multi-Constraint Business Modeling
In a corporate budget analysis model, a system of linear inequalities is used to define the 'allowable spending zone' for two separate departments. Graphically, the solution set for this system is correctly identified as:
A quality control engineer uses a system of linear inequalities to define the acceptable ranges for temperature () and pressure () in a manufacturing process. Unlike a system of linear equations which typically has one unique solution point, the solution set for the engineer's system of inequalities consists of:
Determining Whether an Ordered Pair is a Solution of a System of Linear Inequalities
Solving by Graphing
Learn After
A warehouse manager is mapping out storage constraints using a system of two inequalities: x - 2y < 5 and y > -4. When graphing this system on a coordinate plane, how should the boundary lines be drawn to correctly represent these strict inequalities?
A technician is graphing the system of inequalities x - 2y < 5 and y > -4 to determine a safe operating range for equipment. Arrange the following steps in the correct order to solve this system graphically.
An operations manager is using a coordinate plane to map out a shipping 'safety zone' defined by the system of inequalities {x - 2y < 5, y > -4}. True or False: The point where the two boundary lines intersect is included as a valid solution in the shaded shipping zone.
An environmental safety officer is mapping a 'safe zone' for chemical storage using the system of inequalities {x - 2y < 5, y > -4}. Match each component of the graphical solution with its correct description or characteristic based on the system's properties.
An industrial safety officer is using a coordinate plane to map a 'safe operation zone' defined by the system of inequalities {x - 2y < 5, y > -4}. Because both inequalities use strict comparison symbols (< and >), the boundary lines for the region must be drawn as ________ lines to show that the points on the lines themselves are not part of the safe zone.
Logistics Safety Zone Mapping
Defining the Solution Region for a Storage Map
Facility Safety Zone Mapping Procedure
An inventory specialist is plotting a 'safe storage' zone on a facility floor plan using a coordinate system. The zone is defined by the system of inequalities {x - 2y < 5, y > -4}. When plotting the boundary line for the equation x - 2y = 5, which of the following are the correct intercepts to mark on the grid?
A facility manager is mapping a 'safe operation zone' on a floor plan using the system of inequalities . When plotting the boundary line for the constraint , which of the following correctly describes the equation and orientation of that boundary line?