Question

What is the classification of each system of equations?

4x - 2y = 10; 2x - y = 5
a. Consistent independent
b. Consistent dependent
c. Inconsistent
d. None of the above

Answer 1

The system of equations is consistent dependent.

Step-by-step explanation:

The given system of equations is:

4x - 2y = 10

2x - y = 5

To determine the classification of the system, we need to solve the equations. We can use either substitution or elimination method. Let's use the elimination method:

Multiply the second equation by 2:

4x - 2y = 10

4x - 2y = 10

Now subtract the second equation from the first equation:

4x - 2y - (4x - 2y) = 10 - 10

0 = 0

Since the resulting equation is always true (0 = 0), the system of equations is consistent dependent. Therefore, the correct answer is b. Consistent dependent.