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Which describes the system of equations below? $\newline$ $y = \frac{8}{7}x - 8$ $\newline$ $y = -\frac{5}{6}x + \frac{10}{9}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)consistent and independent $\newline$ (C)inconsistent $\newline$

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Classify a system of equations

Full solution

Q. Which describes the system of equations below?

\newline

y = \frac{8}{7}x - 8

\newline

y = -\frac{5}{6}x + \frac{10}{9}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)consistent and independent

\newline

(C)inconsistent

\newline

Identify slopes: Step $1$ : Identify the slopes of both equations. $\newline$ For $y = \frac{8}{7}x - 8$ , the slope is $\frac{8}{7}$ . $\newline$ For $y = -\frac{5}{6}x + \frac{10}{9}$ , the slope is $-\frac{5}{6}$ . $\newline$ Since $\frac{8}{7}$ is not equal to $-\frac{5}{6}$ , the slopes are different.
Different slopes: Step $2$ : Since the slopes are different, the lines represented by these equations will intersect at exactly one point. $\newline$ This means the system of equations has one solution where the lines cross each other.
One point intersection: Step $3$ : Choose the option that describes the system of equations. $\newline$ Since the lines intersect at one point, the system is consistent (because it has at least one solution) and independent (because it has exactly one solution).

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