To solve the system of equations using substitution, we'll follow these steps:
1. Identify the given system of equations:
[tex]\[
\begin{array}{l}
15x - 5y = -20 \\
y = 3x + 4
\end{array}
\][/tex]
2. Substitute the expression for [tex]\( y \)[/tex] from the second equation into the first equation:
[tex]\[
15x - 5(3x + 4) = -20
\][/tex]
3. Expand and simplify the substituted equation:
[tex]\[
15x - 5(3x + 4) = 15x - 15x - 20 = -20
\][/tex]
4. Combine like terms:
[tex]\[
15x - 15x - 20 = -20
\][/tex]
5. Simplify the equation:
[tex]\[
-20 = -20
\][/tex]
Since the resulting statement [tex]\( -20 = -20 \)[/tex] is always true, this indicates that the two equations are actually the same line, meaning every solution to one equation is also a solution to the other. Therefore, there are infinitely many solutions to this system.
So, the answer is:
Infinitely Many Solutions
