Solve the system by the method of your choice.
left brace Start 2 By 1 Matrix 1st Row 1st Column x equals 5 y minus 4 2nd Row 1st Column 3 x minus 15 y equals negative 12 EndMatrix
 


To solve the system of equations:

\[
\begin{cases}
x = 5y - 4 \\
3x - 15y = -12
\end{cases}
\]

we can use the substitution method. Here are the steps:

1. From the first equation, \( x = 5y - 4 \), we already have \( x \) expressed in terms of \( y \).
2. Substitute \( x = 5y - 4 \) into the second equation \( 3x - 15y = -12 \):

\[ 3(5y - 4) - 15y = -12 \]

3. Simplify the equation:

\[ 15y - 12 - 15y = -12 \]

4. Combine like terms:

\[ -12 = -12 \]

This is an identity, which means that the system has infinitely many solutions. This occurs when the two equations represent the same line.

### Conclusion:
The system of equations has infinitely many solutions because the equations are dependent and represent the same line.

Would you like details or have any questions? Here are 5 more questions you can ask:

1. How do you solve a system of equations using the elimination method?
2. Can you graphically demonstrate why the system has infinitely many solutions?
3. How can you tell if a system of equations is dependent?
4. What are some real-world applications of solving systems of equations?
5. Can you explain the differences between consistent, inconsistent, and dependent systems?

**Tip:** When solving systems of equations, always check if the equations represent the same line (dependent) or parallel lines (inconsistent) to understand the nature of the solutions.

Discover how to solve the system of equations x = 5y - 4 and 3x - 15y = -12 using the substitution method. This guide explains that the system has infinitely many solutions due to the equations being dependent. Suitable for students in Grades 9-12.

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