How many solutions does the system of equations below have? y = –4x + 4/3 y = –4x + 8/3 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Slopes: Analyze the slopes of both equations. The slope of the first equation (y = –4x + 4/3) is -4. The slope of the second equation (y = –4x + 8/3) is also -4. Since both slopes are equal, the lines are either parallel or the same line.Compare Y-Intercepts: Compare the y-intercepts of both equations. The y-intercept of the first equation is 4/3. The y-intercept of the second equation is 8/3. Since the y-intercepts are different, the lines are parallel and do not intersect.Determine Number of 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? $\newline$ $y = -4x + \frac{4}{3}$ $\newline$ $y = -4x + \frac{8}{3}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Algebra 1

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 = -4x + \frac{4}{3}

\newline

y = -4x + \frac{8}{3}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Slopes: Analyze the slopes of both equations. $\newline$ The slope of the first equation $y = -4x + \frac{4}{3}$ is $-4$ . $\newline$ The slope of the second equation $y = -4x + \frac{8}{3}$ is also $-4$ . $\newline$ Since both slopes are equal, the lines are either parallel or the same line.
Compare Y-Intercepts: Compare the $y$ -intercepts of both equations. $\newline$ The $y$ -intercept of the first equation is $\frac{4}{3}$ . $\newline$ The $y$ -intercept of the second equation is $\frac{8}{3}$ . $\newline$ Since the $y$ -intercepts are different, the lines are parallel and do not intersect.
Determine Number of 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.