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Which describes the system of equations below? $\newline$ $y = 10x - 10$ $\newline$ $y = \frac{9}{2}x - \frac{7}{4}$ $\newline$ 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 = 10x - 10

\newline

y = \frac{9}{2}x - \frac{7}{4}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Identify Slopes: We have the system of equations: $\newline$ $y = 10x - 10$ $\newline$ $y = \frac{9}{2}x - \frac{7}{4}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 10x - 10$ , the slope is $10$ . $\newline$ In $y = \frac{9}{2}x - \frac{7}{4}$ , the slope is $\frac{9}{2}$ . $\newline$ Since $10$ is not equal to $\frac{9}{2}$ , the slopes of both equations are different.
Check for Parallel Lines: Since the slopes are different, the lines represented by these equations are not parallel. This means they will intersect at some point on the graph.
Determine Consistency: Because the lines intersect at one point, the system of equations has one solution. This means the system is consistent and the equations are independent.

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