How many solutions does the system have? {[y=-7x+8],[y=-7x-8]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

Question Prompt: Question prompt: Determine the number of solutions for the given system of equations.Analyze Equations: Analyze the given system of equations. The system of equations is: y = -7x + 8 y = -7x - 8 To determine the number of solutions, we need to compare the slopes and y-intercepts of the two lines.Identify Parameters: Identify the slopes and y-intercepts of the two equations. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. For the first equation, y = -7x + 8, the slope (m) is -7 and the y-intercept (b) is 8. For the second equation, y = -7x - 8, the slope (m) is also -7 and the y-intercept (b) is -8.Compare Slopes and Intercepts: Compare the slopes and y-intercepts. Both lines have the same slope of -7, but different y-intercepts (8 and -8). Since the slopes are the same but the y-intercepts are different, the lines are parallel to each other.Conclude Number of Solutions: Conclude the number of solutions based on the comparison. Parallel lines never intersect, so there are no points that satisfy both equations simultaneously. Therefore, the system of equations has no solutions.

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How many solutions does the system have?

{[y=-7x+8],[y=-7x-8]:}
Choose 1 answer:
(A) Exactly one solution
(B) No solutions
(c) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} y=-7 x+8 \\ y=-7 x-8 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

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Algebra 2

Find the number of solutions to a system of equations

Full solution

Q. How many solutions does the system have?

\newline

\left\{\begin{array}{l} y=-7 x+8 \\ y=-7 x-8 \end{array}\right.

\newline

Choose

1

answer:

\newline

(A) Exactly one solution

\newline

(B) No solutions

\newline

Question Prompt: Question prompt: Determine the number of solutions for the given system of equations.
Analyze Equations: Analyze the given system of equations. $\newline$ The system of equations is: $\newline$ $y = -7x + 8$ $\newline$ $y = -7x - 8$ $\newline$ To determine the number of solutions, we need to compare the slopes and $y$ -intercepts of the two lines.
Identify Parameters: Identify the slopes and y-intercepts of the two equations. $\newline$ The slope-intercept form of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. $\newline$ For the first equation, $y = -7x + 8$ , the slope ( $m$ ) is $-7$ and the y-intercept ( $b$ ) is $8$ . $\newline$ For the second equation, $y = -7x - 8$ , the slope ( $m$ ) is also $-7$ and the y-intercept ( $b$ ) is $m$ $2$ .
Compare Slopes and Intercepts: Compare the slopes and $y$ -intercepts. Both lines have the same slope of $-7$ , but different $y$ -intercepts ( $8$ and $-8$ ). Since the slopes are the same but the $y$ -intercepts are different, the lines are parallel to each other.
Conclude Number of Solutions: Conclude the number of solutions based on the comparison. Parallel lines never intersect, so there are no points that satisfy both equations simultaneously. Therefore, the system of equations has no solutions.