How many solutions does the system of equations below have? y = 4x − 2/5 y = 4x + 6/5 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations. The system of equations is: y = 4x − 2/5 y = 4x + 6/5 Both equations have the same slope, which is 4. This means that the lines are parallel. Since they have different y-intercepts (−2/5 and +6/5), the lines will never intersect.Conclude Solutions: Conclude the number of solutions based on the analysis. Since the lines are parallel and have different y-intercepts, they will never meet. Therefore, there are no points that satisfy both equations simultaneously.

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How many solutions does the system of equations below have? $\newline$ $y = 4x - \frac{2}{5}$ $\newline$ $y = 4x + \frac{6}{5}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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

\newline

y = 4x - \frac{2}{5}

\newline

y = 4x + \frac{6}{5}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations. $\newline$ The system of equations is: $\newline$ $y = 4x - \frac{2}{5}$ $\newline$ $y = 4x + \frac{6}{5}$ $\newline$ Both equations have the same slope, which is $4$ . This means that the lines are parallel. Since they have different y-intercepts ( $-\frac{2}{5}$ and $+\frac{6}{5}$ ), the lines will never intersect.
Conclude Solutions: Conclude the number of solutions based on the analysis. $\newline$ Since the lines are parallel and have different $y$ -intercepts, they will never meet. Therefore, there are $0$ points that satisfy both equations simultaneously.