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How many solutions does the system of equations below have? $\newline$ $y = \frac{1}{8}x - 6$ $\newline$ $y = \frac{1}{8}x - 6$ $\newline$ Choices: $\newline$ (A) no solution $\newline$ (B) one solution $\newline$ (C) infinitely many solutions

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Find the number of solutions to a system of equations

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Q. How many solutions does the system of equations below have?

\newline

y = \frac{1}{8}x - 6

\newline

y = \frac{1}{8}x - 6

\newline

Choices:

\newline

(A) no solution

\newline

(B) one solution

\newline

(C) infinitely many solutions

Analyze Equations: Step $1$ : Analyze the equations: $\newline$ $y = \frac{1}{8}x - 6$ $\newline$ $y = \frac{1}{8}x - 6$ $\newline$ Check if the slopes are the same or different. $\newline$ Slope of both equations: $\frac{1}{8}$
Compare Y-Intercepts: Step $2$ : Compare the y-intercepts: $\newline$ y-intercept of the first equation: $-6$ $\newline$ y-intercept of the second equation: $-6$ $\newline$ Both y-intercepts are the same.
Determine Solutions: Step $3$ : Determine the number of solutions: $\newline$ Since both equations have the same slope and $y$ -intercept, they represent the same line. Therefore, every point on the line is a solution to both equations.

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