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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

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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 = 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.

More problems from Find the number of solutions to a system of equations

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How many solutions does the system of equations below have?

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7

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Which describes the system of equations below?

\newline

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\newline

y = \frac{1}{7}x - 10

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\newline

\text{[A]consistent and independent}

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\newline

\_\_\_\_

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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

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There are two mystery numbers. The sum of

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Question

A teacher purchased

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