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Which describes the system of equations below? $\newline$ $y = -\frac{9}{10}x + \frac{5}{4}$ $\newline$ $y = -\frac{9}{10}x + \frac{5}{4}$ $\newline$ Choices: $\newline$ (A) inconsistent $\newline$ (B) consistent and dependent $\newline$ (C) consistent and independent

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = -\frac{9}{10}x + \frac{5}{4}

\newline

y = -\frac{9}{10}x + \frac{5}{4}

\newline

Choices:

\newline

(A) inconsistent

\newline

(B) consistent and dependent

\newline

(C) consistent and independent

Analyze Equations: Analyze the given system of equations to determine if they are the same or different. $\newline$ We have: $\newline$ $y = \frac{-9}{10}x + \frac{5}{4}$ $\newline$ $y = \frac{-9}{10}x + \frac{5}{4}$ $\newline$ Check if the slopes of both equations are the same. $\newline$ In $y = \frac{-9}{10}x + \frac{5}{4}$ , the slope is $\frac{-9}{10}$ . $\newline$ In $y = \frac{-9}{10}x + \frac{5}{4}$ , the slope is also $\frac{-9}{10}$ . $\newline$ Since the slopes are the same, we proceed to check the y-intercepts.
Check Slopes: Check if the y-intercepts of both equations are the same. $\newline$ In $y = -\frac{9}{10}x + \frac{5}{4}$ , the y-intercept is $\frac{5}{4}$ . $\newline$ In $y = -\frac{9}{10}x + \frac{5}{4}$ , the y-intercept is also $\frac{5}{4}$ . $\newline$ Since the y-intercepts are the same, we can conclude that the two equations are identical.
Check Y-Intercepts: Determine the type of system based on the findings from steps $1$ and $2$ . Since both the slopes and $y$ -intercepts are the same, the two equations represent the same line. Therefore, the system of equations has an infinite number of solutions, as any solution that works for one equation will also work for the other. This means the system of equations is consistent and dependent.

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