Question

Which of the following classifications fit the following system?2x-y=36x-3y=9Group of answer choicesInconsistent and dependentInconsistent and independentConsistent and dependentConsistent and independent

Answer 1

System of Equations

A system of equations is called consistent if it has at least one solution. It's inconsistent if it has no solutions.

Once determined a system is consistent, it can be classified as dependent or independent.

If only one solution is possible, then it's an independent system. If more than one (or infinitely many) solution(s) are possible, then it's a dependent system.

Let's analyze the system:

2x - y = 3

6x - 3y = 9

If we multiply the first equation by 3, we get exactly the second equation, thus this is not a system of equations, but a single equation with two variables. If we solve for y:

y = 2x - 3

We can give x any value and calculate the corresponding value for y.

For example, for x = 0, y = -3

For x = 1, y = -1

For x = 2, y = 1

There are infinitely many solutions, thus the system is consistent and dependent