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Which describes the system of equations below? $\newline$ $y = -4x + 5$ $\newline$ $y = -\frac{7}{4}x + \frac{3}{2}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = -4x + 5

\newline

y = -\frac{7}{4}x + \frac{3}{2}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify Slopes: We have the following system of equations: $\newline$ $y = -4x + 5$ $\newline$ $y = -\frac{7}{4}x + \frac{3}{2}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = -4x + 5$ , the slope is $-4$ . $\newline$ In $y = -\frac{7}{4}x + \frac{3}{2}$ , the slope is $-\frac{7}{4}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine Intersection: Since the slopes are different, the lines represented by these equations are not parallel. This means they will intersect at some point. $\newline$ Therefore, the system of equations has a unique solution where the two lines intersect.
Consistent and Independent: A system of equations with a unique solution is considered consistent because there is at least one set of values that satisfies both equations. It is also independent because the equations represent different lines that intersect at only one point.

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