How many solutions does the system of equations below have? y = 2/3x − 3 y = 2/3x − 5/6 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations. The system of equations is: y = 2/3x − 3 y = 2/3x − 5/6 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 the two equations to determine the number of solutions.Compare Slopes: Compare the slopes of the two equations. The slope of the first equation is 2/3, and the slope of the second equation is also 2/3. 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 -3, and the y-intercept of the second equation is -5/6. 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, the system of equations has no solution.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many solutions does the system of equations below have? $\newline$ $y = \frac{2}{3}x - 3$ $\newline$ $y = \frac{2}{3}x - \frac{5}{6}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

View step-by-step help

Home

Math Problems

Precalculus

Solve trigonometric equations

Full solution

Q. How many solutions does the system of equations below have?

\newline

y = \frac{2}{3}x - 3

\newline

y = \frac{2}{3}x - \frac{5}{6}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations. $\newline$ The system of equations is: $\newline$ $y = \frac{2}{3}x − 3$ $\newline$ $y = \frac{2}{3}x − \frac{5}{6}$ $\newline$ 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 the 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 $\frac{2}{3}$ , and the slope of the second equation is also $\frac{2}{3}$ . 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 $-3$ , and the $y$ -intercept of the second equation is $-\frac{5}{6}$ . 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, the system of equations has $no$ solution.