Create a system of linear equations.
Explain the steps for solving a system of linear inequalities.
Make a system of linear inequalities problem.
Please help me with this?
14x-7y=21
x+7=19
ok, I will check your explanation of steps for solving.
Sure! I can help you with that.
1. Creating a system of linear equations:
To create a system of linear equations, you need multiple linear equations that are related to each other. The equations should contain variables and constants, and the variables should be raised to the first power only. Here's an example of a system of linear equations:
Equation 1: 2x + 3y = 7
Equation 2: -4x + 5y = 2
2. Steps for solving a system of linear inequalities:
To solve a system of linear inequalities, you need to follow these steps:
Step 1: Graph each inequality separately. This will help you visualize their solution regions on a coordinate plane.
Step 2: Determine the overlapping region where all the solution regions intersect. This overlapping region represents the solution to the system of inequalities.
Step 3: Identify the specific combination of variables (if any) that satisfy all the inequalities simultaneously. This can be done by examining the coordinates within the overlapping region.
3. Creating a system of linear inequalities problem:
Here's an example of a system of linear inequalities problem:
Problem: A manufacturer produces two types of smartphones, A and B. Each unit of type A requires 3 hours of labor and 2 hours of machine time, while each unit of type B requires 2 hours of labor and 1 hour of machine time. The maximum labor hours available per day are 30, and the maximum machine hours available per day are 20. Let x represent the number of units of type A, and y represent the number of units of type B. Write a system of linear inequalities to represent the production limits.
Solution:
Equation 1: 3x + 2y ≤ 30 (Maximum labor hours constraint)
Equation 2: 2x + y ≤ 20 (Maximum machine hours constraint)
These two inequalities outline the constraints for production based on the labor and machine hours available.