Answered

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On your own paper, solve the system of equations using substitution and identify the solution.

[tex]\[
\begin{array}{l}
15x - 5y = -20 \\
y = 3x + 4
\end{array}
\][/tex]

A. (2, -2)
B. (-2, 2)
C. (2, 16)
D. (16, 2)
E. No Solution
F. Infinitely Many Solutions

Sagot :

GinnyAnswer
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
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