How many solutions does the system of equations below have? y = –2x − 10 y = –2x + 4/7 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of equations. The system of equations is: y = –2x − 10 y = –2x + 4/7 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 of the two lines. The slope of the first line is -2 and the slope of the second line is also -2. Since the slopes are equal, the lines are either parallel or the same line.Compare Y-Intercepts: Compare the y-intercepts of the two lines. The y-intercept of the first line is -10 and the y-intercept of the second line is 4/7. Since the y-intercepts are different, the lines are parallel and do not intersect.Determine Solutions: Determine the number of solutions. 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? $\newline$ $y = -2x - 10$ $\newline$ $y = -2x + \frac{4}{7}$ $\newline$ 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 = -2x - 10

\newline

y = -2x + \frac{4}{7}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of equations. $\newline$ The system of equations is: $\newline$ $y = -2x - 10$ $\newline$ $y = -2x + \frac{4}{7}$ $\newline$ 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 of the two lines. $\newline$ The slope of the first line is $-2$ and the slope of the second line is also $-2$ . Since the slopes are equal, the lines are either parallel or the same line.
Compare Y-Intercepts: Compare the y-intercepts of the two lines. $\newline$ The y-intercept of the first line is $-10$ and the y-intercept of the second line is $\frac{4}{7}$ . Since the y-intercepts are different, the lines are parallel and do not intersect.
Determine Solutions: Determine the number of solutions. $\newline$ Since the lines are parallel and have different $y$ -intercepts, they will never intersect. Therefore, there are no solutions to the system of equations.