Question

Use the method of elimination to determine whether the given linear system is consistent or inconsistent?

Answer 1

When using elimination to determine if a linear system is consistent or inconsistent, eliminate terms to simplify the equations, solve for the unknowns, and check if the solution makes sense. A consistent system has viable solutions, while an inconsistent system does not.

Step-by-step explanation:

To determine whether the given linear system is consistent or inconsistent using the method of elimination, you should first list what is given and what can be inferred. Then eliminate terms to simplify the algebra, solving equations for the unknown. Once you find a solution, check to see if it is reasonable.

List the knowns and infer unknowns.Use elimination to simplify the algebra.Solve the equations for the unknown.Check if the solution is reasonable and makes sense with the given problem.

If after elimination the system results in a true statement, like 0=0, that indicates it's consistent, meaning there is at least one set of solutions. An inconsistent system, on the other hand, results in a false statement, like 0=5, which means there are no solutions.

To answer a question related to the equilibrium of a system or to determine a linear regression line equation, similar steps may be applied, but they will involve subject-specific concepts and formulas.

Answer 2

To determine if a linear system is consistent or inconsistent using the method of elimination, identify knowns, eliminate terms to cancel out variables, solve for the remaining variables, and then check the solutions' reasonableness by substituting them into the original equations.

Step-by-step explanation:

To determine whether the given linear system is consistent or inconsistent using the method of elimination, we need to follow a series of steps:

1. Identify the knowns: Read the equations provided in the linear system and note down all the coefficients and constants.
2. Eliminate terms: Manipulate the equations to cancel out one of the variables. This might involve multiplying an equation by a number so that when you add or subtract the equations from each other, one of the variables gets eliminated.
3. Solve the equation: Once a variable is eliminated, solve for the remaining variable.
4. Substitute the value of the found variable into one of the original equations to solve for the other variable.
5. Check the reasonableness: Verify the solution by substituting the values back into the original equations to see if they hold true. If an inconsistency arises, such as a false statement (e.g., 0=5), the system is inconsistent.
6. If both variables have been solved and the solutions make each equation true, the system is consistent.

To simplify this process, one can draw analogies with translational motion equations, where similar elimination strategies are used to solve for unknowns.