How many solutions does the system have? {[y=9x-5],[y=9x+6]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

Analyze slopes of equations: Analyze the slopes of both equations. The slope of the first equation (y = 9x - 5) is 9. The slope of the second equation (y = 9x + 6) is also 9. Since both slopes are equal, we can conclude that the lines are parallel unless they are the same line.Compare y-intercepts: Compare the y-intercepts of both equations. The y-intercept of the first equation (y = 9x - 5) is -5. The y-intercept of the second equation (y = 9x + 6) is 6. Since the y-intercepts are different, the lines are not the same line.Determine number of solutions: Determine the number of solutions. Since the lines have the same slope but different y-intercepts, they will never intersect. Therefore, the system of equations has no solutions.

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How many solutions does the system have?

{[y=9x-5],[y=9x+6]:}
Choose 1 answer:
(A) Exactly one solution
(B) No solutions
(C) Infinitely many solutions

How many solutions does the system have? $\newline$ $\left\{\begin{array}{l} y=9 x-5 \\ y=9 x+6 \end{array}\right.$ $\newline$ Choose $1$ answer: $\newline$ (A) Exactly one solution $\newline$ (B) No solutions $\newline$ (C) Infinitely many solutions

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Math Problems

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=9 x-5 \\ y=9 x+6 \end{array}\right.

\newline

Choose

1

answer:

\newline

(A) Exactly one solution

\newline

(B) No solutions

\newline

Analyze slopes of equations: Analyze the slopes of both equations. $\newline$ The slope of the first equation $y = 9x - 5$ is $9$ . $\newline$ The slope of the second equation $y = 9x + 6$ is also $9$ . $\newline$ Since both slopes are equal, we can conclude that the lines are parallel unless they are the same line.
Compare y-intercepts: Compare the y-intercepts of both equations. $\newline$ The y-intercept of the first equation $y = 9x - 5$ is $-5$ . $\newline$ The y-intercept of the second equation $y = 9x + 6$ is $6$ . $\newline$ Since the y-intercepts are different, the lines are not the same line.
Determine number of solutions: Determine the number of solutions. $\newline$ Since the lines have the same slope but different $y$ -intercepts, they will never intersect. $\newline$ Therefore, the system of equations has no solutions.