How many solutions does the system of equations below have? y = 6x + 7 y = 6x + 7 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of equations: y = 6x + 7 y = 6x + 7 Are the slopes of the two equations the same or different? Slope of the first equation: 6 Slope of the second equation: 6 The slopes of both equations are the same.Compare Slopes: Compare the y-intercepts of the two equations: y-intercept of the first equation: 7 y-intercept of the second equation: 7 The y-intercepts of both equations are the same.Compare Y-Intercepts: Determine the number of solutions to the system of equations: Since both equations have the same slope and the same y-intercept, they represent the same line. Therefore, the system of equations has infinitely many solutions, as every point on the line is a solution to both equations.

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? $\newline$ $y = 6x + 7$ $\newline$ $y = 6x + 7$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

View step-by-step help

Home

Math Problems

Algebra 1

Find the number of solutions to a system of equations

Full solution

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

\newline

y = 6x + 7

\newline

y = 6x + 7

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of equations: $\newline$ $y = 6x + 7$ $\newline$ $y = 6x + 7$ $\newline$ Are the slopes of the two equations the same or different? $\newline$ Slope of the first equation: $6$ $\newline$ Slope of the second equation: $6$ $\newline$ The slopes of both equations are the same.
Compare Slopes: Compare the $y$ -intercepts of the two equations: $\newline$ $y$ -intercept of the first equation: $7$ $\newline$ $y$ -intercept of the second equation: $7$ $\newline$ The $y$ -intercepts of both equations are the same.
Compare Y-Intercepts: Determine the number of solutions to the system of equations: $\newline$ Since both equations have the same slope and the same $y$ -intercept, they represent the same line. Therefore, the system of equations has infinitely many solutions, as every point on the line is a solution to both equations.