Question

Determine whether the system is consistent, inconsistent, or dependent. 5x - y = 4 -5y + y = -4

Answer 1

Upon correcting the second equation and solving the system, it is found to be consistent and independent, with a unique solution of x = 1 and y = 1.

Step-by-step explanation:

To determine whether the system of equations is consistent, inconsistent, or dependent, let us examine the equations given:

• 5x - y = 4
• -5y + y = -4

First, we notice that the second equation seems to have a typo, as it contains two 'y' terms on the left side. If we take the equation as it is, -5y + y simplifies to -4y.

Now, our system is:

• 5x - y = 4
• -4y = -4

Solving the second equation for 'y' we get y = 1.

Substituting 'y' back into the first equation, we have:

• 5x - 1 = 4

Solving this for 'x' gives us x = 1.

Since we found a unique solution for 'x' and 'y', the system is consistent and independent.