How many solutions does the system of equations below have? y = –6x − 9 y = –6x + 7/8 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze System of Equations: Analyze the given system of equations to determine the number of solutions. The system of equations is: y = –6x − 9 y = –6x + 7/8 Both equations are in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. To determine the number of solutions, we need to compare the slopes (m) and y-intercepts (b) of the two lines.Compare Slopes: Compare the slopes of the two equations. The slope of the first equation is –6, and the slope of the second equation is also –6. Since the slopes are equal, the lines are either parallel or the same line.Compare Y-Intercepts: Compare the y-intercepts of the two equations. The y-intercept of the first equation is –9, and the y-intercept of the second equation is 7/8. Since the y-intercepts are different, the lines are parallel and do not intersect.Conclude Number of Solutions: Conclude the number of solutions based on the comparison of slopes and y-intercepts. Since the lines are parallel and have different y-intercepts, they will never intersect. Therefore, the system of equations has no solution.

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How many solutions does the system of equations below have? $\newline$ $y = -6x - 9$ $\newline$ $y = -6x + \frac{7}{8}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Grade 8

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 = -6x - 9

\newline

y = -6x + \frac{7}{8}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze System of Equations: Analyze the given system of equations to determine the number of solutions. $\newline$ The system of equations is: $\newline$ $y = -6x - 9$ $\newline$ $y = -6x + \frac{7}{8}$ $\newline$ Both equations are in the slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. To determine the number of solutions, we need to compare the slopes ( $m$ ) and y-intercepts ( $b$ ) of the two lines.
Compare Slopes: Compare the slopes of the two equations. $\newline$ The slope of the first equation is $-6$ , and the slope of the second equation is also $-6$ . Since the slopes are equal, the lines are either parallel or the same line.
Compare Y-Intercepts: Compare the y-intercepts of the two equations. $\newline$ The y-intercept of the first equation is $-9$ , and the y-intercept of the second equation is $\frac{7}{8}$ . Since the y-intercepts are different, the lines are parallel and do not intersect.
Conclude Number of Solutions: Conclude the number of solutions based on the comparison of slopes and $y$ -intercepts. $\newline$ Since the lines are parallel and have different $y$ -intercepts, they will never intersect. Therefore, the system of equations has $0$ solution.