Which describes the system of equations below? y = –5x + 7/2 y = 1/7x + 9/7 Choices: (A)consistent and independent (B)consistent and dependent (C)inconsistent

Identify Slopes: We have the following system of equations: y = –5x + 7/2 y = 1/7x + 9/7 Identify whether the slopes of both the equations are the same. In y = –5x + 7/2, the slope is –5. In y = 1/7x + 9/7, the slope is 1/7. No, the slopes of both the equations are not the same.Determine Intersection: Since the slopes are different, the lines are not parallel and will intersect at exactly one point. This means the system of equations has one unique solution.Check System Type: Choose the option which describes the given system of equations. Since the slopes are different and there is one unique solution, the system of equations is consistent and independent.

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Which describes the system of equations below? $\newline$ $y = -5x + \frac{7}{2}$ $\newline$ $y = \frac{1}{7}x + \frac{9}{7}$ $\newline$ 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 = -5x + \frac{7}{2}

\newline

y = \frac{1}{7}x + \frac{9}{7}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)consistent and dependent

\newline

(C)inconsistent

Identify Slopes: We have the following system of equations: $\newline$ $y = -5x + \frac{7}{2}$ $\newline$ $y = \frac{1}{7}x + \frac{9}{7}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = -5x + \frac{7}{2}$ , the slope is $-5$ . $\newline$ In $y = \frac{1}{7}x + \frac{9}{7}$ , the slope is $\frac{1}{7}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine Intersection: Since the slopes are different, the lines are not parallel and will intersect at exactly one point. This means the system of equations has one unique solution.
Check System Type: Choose the option which describes the given system of equations. $\newline$ Since the slopes are different and there is one unique solution, the system of equations is consistent and independent.