Solve the following system of equations. Classify it as CONSISTENT (INDEPENDENT or DEPENDENT) or INCONSISTENT.
$y=5x-17$
$15x-3y=51$

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

Answer: (B)

Verified step by step guidance

1. Start by writing down the system of equations: \( y = 5x - 17 \) and \( 15x - 3y = 51 \).
2. Substitute the expression for \( y \) from the first equation into the second equation. This gives: \( 15x - 3(5x - 17) = 51 \).
3. Distribute the \(-3\) across the terms in the parentheses: \( 15x - 15x + 51 = 51 \).
4. Simplify the equation: \( 0x + 51 = 51 \), which simplifies to \( 51 = 51 \).
5. Since the equation \( 51 = 51 \) is always true, the system is consistent and dependent, meaning there are infinitely many solutions.