How many solutions does the system of equations below have? y = –3x + 3 y = –3x − 7/5 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of equations. We have two equations: 1. y = –3x + 3 2. y = –3x – 7/5 Both equations are in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. Compare the slopes of the two lines.Compare Slopes: Compare the slopes. The slope of the first equation is -3, and the slope of the second equation is also -3. Since the slopes are equal, the lines are either parallel or the same line.Compare Y-Intercepts: Compare the y-intercepts. The y-intercept of the first equation is 3, and the y-intercept of the second equation is -7/5. Since the y-intercepts are different, the lines are parallel and do not intersect.Determine Solutions: Determine the number of solutions. Parallel lines never intersect, so there are no points that satisfy both equations simultaneously. Therefore, the system of equations has no solution.

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How many solutions does the system of equations below have? $\newline$ $y = -3x + 3$ $\newline$ $y = -3x - \frac{7}{5}$ $\newline$ 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 = -3x + 3

\newline

y = -3x - \frac{7}{5}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of equations. $\newline$ We have two equations: $\newline$ $1$ . $y = -3x + 3$ $\newline$ $2$ . $y = -3x - \frac{7}{5}$ $\newline$ Both equations are in the slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. Compare the slopes of the two lines.
Compare Slopes: Compare the slopes. $\newline$ The slope of the first equation is $-3$ , and the slope of the second equation is also $-3$ . Since the slopes are equal, the lines are either parallel or the same line.
Compare Y-Intercepts: Compare the y-intercepts. $\newline$ The y-intercept of the first equation is $3$ , and the y-intercept of the second equation is $-\frac{7}{5}$ . Since the y-intercepts are different, the lines are parallel and do not intersect.
Determine Solutions: Determine the number of solutions. $\newline$ Parallel lines never intersect, so there are no points that satisfy both equations simultaneously. Therefore, the system of equations has no solution.