Which describes the system of equations below? y = 5/7x + 3 y = 5/7x + 3 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Identify Slopes: We have the system of equations: y = (5/7)x + 3 y = (5/7)x + 3 First, we need to identify whether the slopes of both equations are the same. In y = (5/7)x + 3, the slope is 5/7. In y = (5/7)x + 3, the slope is also 5/7.Identify Y-Intercepts: Next, we need to identify whether the y-intercepts of both equations are the same. In y = (5/7)x + 3, the y-intercept is 3. In y = (5/7)x + 3, the y-intercept is also 3.Determine Line Equality: Since both the slopes and y-intercepts of the equations are the same, the lines represented by these equations are identical. This means that every solution to one equation is also a solution to the other, and there are infinitely many solutions.Classify System of Equations: Choose the option which describes the given system of equations. Since the slopes and y-intercepts are the same, the system of equations is consistent and dependent. This means that the two equations represent the same line.

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Which describes the system of equations below? $\newline$ $y = \frac{5}{7}x + 3$ $\newline$ $y = \frac{5}{7}x + 3$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Algebra 1

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = \frac{5}{7}x + 3

\newline

y = \frac{5}{7}x + 3

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify Slopes: We have the system of equations: $\newline$ $y = \frac{5}{7}x + 3$ $\newline$ $y = \frac{5}{7}x + 3$ $\newline$ First, we need to identify whether the slopes of both equations are the same. $\newline$ In $y = \frac{5}{7}x + 3$ , the slope is $\frac{5}{7}$ . $\newline$ In $y = \frac{5}{7}x + 3$ , the slope is also $\frac{5}{7}$ .
Identify Y-Intercepts: Next, we need to identify whether the y-intercepts of both equations are the same. $\newline$ In $y = \frac{5}{7}x + 3$ , the y-intercept is $3$ . $\newline$ In $y = \frac{5}{7}x + 3$ , the y-intercept is also $3$ .
Determine Line Equality: Since both the slopes and $y$ -intercepts of the equations are the same, the lines represented by these equations are identical. This means that every solution to one equation is also a solution to the other, and there are infinitely many solutions.
Classify System of Equations: Choose the option which describes the given system of equations. Since the slopes and $y$ -intercepts are the same, the system of equations is consistent and dependent. This means that the two equations represent the same line.