How many solutions does the system of equations below have? y = 1/3x + 1/10 y = 1/3x + 1/10 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Slopes: Analyze the system of equations: y = 1/3x + 1/10 y = 1/3x + 1/10 Are the slopes the same or different? Slope of the first equation: 1/3 Slope of the second equation: 1/3 Slopes of the equations are the same.Analyze Y-Intercepts: Analyze the system of equations: y = 1/3x + 1/10 y = 1/3x + 1/10 Are the y-intercepts the same or different? y-intercept of the first equation: 1/10 y-intercept of the second equation: 1/10 y-intercepts of the equations are the same.Determine Solutions: Determine the number of solutions to the system of equations: The system of equations has the same slope and the same y-intercept. Therefore, the lines represented by these equations are identical. The system of equations has infinitely many solutions.

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How many solutions does the system of equations below have? $\newline$ $y = \frac{1}{3}x + \frac{1}{10}$ $\newline$ $y = \frac{1}{3}x + \frac{1}{10}$ $\newline$ 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 = \frac{1}{3}x + \frac{1}{10}

\newline

y = \frac{1}{3}x + \frac{1}{10}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Slopes: Analyze the system of equations: $\newline$ $y = \frac{1}{3}x + \frac{1}{10}$ $\newline$ $y = \frac{1}{3}x + \frac{1}{10}$ $\newline$ Are the slopes the same or different? $\newline$ Slope of the first equation: $\frac{1}{3}$ $\newline$ Slope of the second equation: $\frac{1}{3}$ $\newline$ Slopes of the equations are the same.
Analyze Y-Intercepts: Analyze the system of equations: $\newline$ $y = \frac{1}{3}x + \frac{1}{10}$ $\newline$ $y = \frac{1}{3}x + \frac{1}{10}$ $\newline$ Are the y-intercepts the same or different? $\newline$ y-intercept of the first equation: $\frac{1}{10}$ $\newline$ y-intercept of the second equation: $\frac{1}{10}$ $\newline$ y-intercepts of the equations are the same.
Determine Solutions: Determine the number of solutions to the system of equations: $\newline$ The system of equations has the same slope and the same $y$ -intercept. $\newline$ Therefore, the lines represented by these equations are identical. $\newline$ The system of equations has infinitely many solutions.