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How many solutions does the system of equations below have? $\newline$ $y = 8x + 7$ $\newline$ $y = 8x + 7$ $\newline$ 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 = 8x + 7

\newline

y = 8x + 7

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Compare y-intercepts: Compare the y-intercepts of the two equations: $\newline$ y = $8$ x + $7$ $\newline$ y = $8$ x + $7$ $\newline$ y-intercept of the first equation: $7$ $\newline$ y-intercept of the second equation: $7$ $\newline$ The y-intercepts of both equations are the same.
Determine number of solutions: Determine the number of solutions to the system of equations: $\newline$ Since both equations have the same slope and the same $y$ -intercept, they represent the same line. Therefore, every point on the line is a solution to both equations. $\newline$ The system of equations has infinitely many solutions.

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