Question

Without graphing, classify the system as independent, dependent, or inconsistent.

{2x=y−74x−2y+4=0}
A. independent
B. dependent
C. inconsistent

Answer 1

To classify the system, we solve the equations and determine if a solution exists or not. In this case, the system is inconsistent because the equations lead to a contradiction.

Step-by-step explanation:

To classify the system without graphing, we can use the technique of solving the system of equations.

Given the system:

{2x = y - 7
4x - 2y + 4 = 0}

We can solve the first equation for y:

y = 2x + 7

Substitute this value of y into the second equation:

4x - 2(2x + 7) + 4 = 0

Simplify the equation:

4x - 4x - 14 + 4 = 0

-14 = 0

This is a contradiction since -14 does not equal 0.

Therefore, the system is inconsistent.

The correct answer is C. inconsistent.