How many solutions does the system of equations below have? y = –4x + 10 y = –4x − 4/9 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations. We have two equations: 1. y = –4x + 10 2. y = –4x – 4/9 Both equations are in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. We can compare the slopes and y-intercepts of these two equations to determine the number of solutions.Compare Slopes: Compare the slopes of the two equations. The slope of the first equation is -4, and the slope of the second equation is also -4. 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 10, and the y-intercept of the second equation is -4/9. 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. Since the lines are parallel and have different y-intercepts, they will never intersect. Therefore, there are no solutions to the system of equations.

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How many solutions does the system of equations below have? $\newline$ $y = -4x + 10$ $\newline$ $y = -4x - \frac{4}{9}$ $\newline$ 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 + 10

\newline

y = -4x - \frac{4}{9}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations. $\newline$ We have two equations: $\newline$ $1$ . $y = -4x + 10$ $\newline$ $2$ . $y = -4x - \frac{4}{9}$ $\newline$ Both equations are in the slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. We can compare the slopes and y-intercepts of these two equations to determine the number of solutions.
Compare Slopes: Compare the slopes of the two equations. $\newline$ The slope of the first equation is $-4$ , and the slope of the second equation is also $-4$ . 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 $10$ , and the $y$ -intercept of the second equation is $-\frac{4}{9}$ . 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. $\newline$ Since the lines are parallel and have different $y$ -intercepts, they will never intersect. Therefore, there are no solutions to the system of equations.