Question

Solve the following system of equations. State whether the system is consistent and independent, consistent and dependent, or inconsistent. -4x+7y=28 4x-7y=32

Answer 1

Answer:

Inconsistent

Step-by-step explanation:

If a system has at least one solution, it is said to be consistent.

If a consistent system has exactly one solution, it is independent.

If a consistent system has an infinite number of solutions, it is dependent.

A system of equations is called an inconsistent system of equations if there is no solution.

Given the system of two equations

$\left\{\begin{array}{l}-4x+7y=28\\ \\4x-7y=32\end{array}\right.$

Add these two equations:

$(-4x+7y)+(4x-7y)=28+32\\ \\-4x+7y+4x-7y=60\\ \\(-4x+4x)+(7y-7y)=60\\ \\0=60$

This is false statement, hence, the system of two equations has no solution and is inconsistent.