Which describes the system of equations below? y = 8/7x − 8 y = –5/6x + 10/9 Choices: (A)consistent and dependent (B)consistent and independent (C)inconsistent

Identify slopes: Step 1: Identify the slopes of both equations. For y = 8/7x - 8, the slope is 8/7. For y = -5/6x + 10/9, the slope is -5/6. Since 8/7 is not equal to -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. 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. 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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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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Algebra 1

Classify a system of equations

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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).