How many solutions does the system of equations below have? y = 3x + 4/5 y = 3x + 7/2 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 = 3x + 4/5) is 3. The slope of the second equation (y = 3x + 7/2) is also 3. 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 4/5. The y-intercept of the second equation is 7/2. 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? $\newline$ $y = 3x + \frac{4}{5}$ $\newline$ $y = 3x + \frac{7}{2}$ $\newline$ 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 = 3x + \frac{4}{5}

\newline

y = 3x + \frac{7}{2}

\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 $y = 3x + \frac{4}{5}$ is $3$ . $\newline$ The slope of the second equation $y = 3x + \frac{7}{2}$ is also $3$ . $\newline$ 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 $\frac{4}{5}$ . $\newline$ The y-intercept of the second equation is $\frac{7}{2}$ . $\newline$ 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. $\newline$ Therefore, the system of equations has no solution.