Which describes the system of equations below? y = 5/2x + 9 y = 5/2x + 9 Choices: (A)consistent and independent (B)consistent and dependent (C)inconsistent

Compare slopes: We have the system of equations: y = (5/2)x + 9 y = (5/2)x + 9 First, we need to compare the slopes of both equations. In y = (5/2)x + 9, the slope is 5/2. In y = (5/2)x + 9, the slope is also 5/2.Compare y-intercepts: Next, we compare the y-intercepts of both equations. In y = (5/2)x + 9, the y-intercept is 9. In y = (5/2)x + 9, the y-intercept is also 9.Identical lines: Since both the slopes and y-intercepts of the two equations are the same, the lines represented by these equations are identical. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions.Choose correct option: Choose the option that correctly describes the given system of equations. Since the lines are identical, the system is consistent (it has at least one solution) and dependent (the equations are essentially the same, so they depend on each other for all their solutions).

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Which describes the system of equations below? $\newline$ $y = \frac{5}{2}x + 9$ $\newline$ $y = \frac{5}{2}x + 9$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)consistent and dependent $\newline$ (C)inconsistent

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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}{2}x + 9

\newline

y = \frac{5}{2}x + 9

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Compare slopes: We have the system of equations: $\newline$ y = $(\frac{5}{2})x + 9$ $\newline$ y = $(\frac{5}{2})x + 9$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = (\frac{5}{2})x + 9$ , the slope is $\frac{5}{2}$ . $\newline$ In $y = (\frac{5}{2})x + 9$ , the slope is also $\frac{5}{2}$ .
Compare y-intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = \frac{5}{2}x + 9$ , the y-intercept is $9$ . $\newline$ In $y = \frac{5}{2}x + 9$ , the y-intercept is also $9$ .
Identical lines: Since both the slopes and $y$ -intercepts of the two equations are the same, the lines represented by these equations are identical. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions.
Choose correct option: Choose the option that correctly describes the given system of equations. Since the lines are identical, the system is consistent (it has at least one solution) and dependent (the equations are essentially the same, so they depend on each other for all their solutions).