Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.
$2x+8y=7$
$x+4y=19$

• A. Consistent and Independent
• B. Consistent and Dependent
• C. Inconsistent

Answer: (C)

Verified step by step guidance

1. Step 1: Write down the given system of equations. The first equation is 2x + 8y = 7, and the second equation is x + 4y = 19.
2. Step 2: Simplify the first equation by dividing all terms by 2 to make it easier to compare with the second equation. This gives x + 4y = 3.5.
3. Step 3: Compare the simplified first equation (x + 4y = 3.5) with the second equation (x + 4y = 19).
4. Step 4: Notice that the left-hand sides of both equations are identical, but the right-hand sides are different (3.5 ≠ 19).
5. Step 5: Conclude that the system of equations is inconsistent because the equations represent parallel lines that never intersect, meaning there is no solution.