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. Step 1: Start by examining the given system of equations. The first equation is y = 5x - 17, and the second equation is 15x - 3y = 51.
2. Step 2: Substitute the expression for y from the first equation into the second equation. This means replacing y in the second equation with 5x - 17.
3. Step 3: Simplify the second equation after substitution. Distribute and combine like terms to see if the equation holds true or results in a contradiction.
4. Step 4: Analyze the resulting equation. If it simplifies to a true statement (like 0 = 0), the system is consistent and dependent. If it simplifies to a false statement (like 0 = 5), the system is inconsistent.
5. Step 5: If the equations are consistent and dependent, it means they represent the same line, and there are infinitely many solutions. If they are consistent and independent, they intersect at a single point.