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: Start by writing down the given system of equations. The first equation is \(2x + 8y = 7\) and the second equation is \(x + 4y = 19\).
2. Step 2: To solve the system, we can use the method of elimination. First, multiply the second equation by 2 to align the coefficients of \(x\) in both equations. This gives us \(2x + 8y = 38\).
3. Step 3: Now, subtract the first equation \(2x + 8y = 7\) from the modified second equation \(2x + 8y = 38\). This will eliminate \(x\) and \(y\) terms, resulting in \(0 = 31\).
4. Step 4: The equation \(0 = 31\) is a contradiction, indicating that there is no solution to the system of equations. This means the system is inconsistent.
5. Step 5: Since the system is inconsistent, it does not have any solutions, and therefore cannot be classified as consistent (independent or dependent).