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

Analyze Equations: Analyze the given system of equations: y = x + 7 y = x + 7 Are the slopes of the two equations the same or different? Slope of the first equation: 1 Slope of the second equation: 1 Since both slopes are equal, we can say that the lines are parallel or the same line.Compare Y-Intercepts: Compare the y-intercepts of the two equations: y-intercept of the first equation: 7 y-intercept of the second equation: 7 Since both y-intercepts are equal, we can conclude that the lines not only have the same slope but also the same y-intercept.Determine Solutions: Determine the number of solutions to the system of equations: Since the system of equations has the same slope and the same y-intercept, the lines are coincident, meaning they lie on top of each other. Therefore, the system of equations has infinitely many solutions, as every point on the line y = x + 7 is a solution to both equations.

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

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Algebra 1

Find the number of solutions to a system of equations

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

\newline

y = x + 7

\newline

y = x + 7

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of equations: $\newline$ $y = x + 7$ $\newline$ $y = x + 7$ $\newline$ Are the slopes of the two equations the same or different? $\newline$ Slope of the first equation: $1$ $\newline$ Slope of the second equation: $1$ $\newline$ Since both slopes are equal, we can say that the lines are parallel or the same line.
Compare Y-Intercepts: Compare the y-intercepts of the two equations: $\newline$ y-intercept of the first equation: $7$ $\newline$ y-intercept of the second equation: $7$ $\newline$ Since both y-intercepts are equal, we can conclude that the lines not only have the same slope but also the same y-intercept.
Determine Solutions: Determine the number of solutions to the system of equations: $\newline$ Since the system of equations has the same slope and the same $y$ -intercept, the lines are coincident, meaning they lie on top of each other. $\newline$ Therefore, the system of equations has infinitely many solutions, as every point on the line $y = x + 7$ is a solution to both equations.