Which describes the system of equations below? y = 7/9x − 5/6 y = 9/4x + 2/3 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Identify slopes of equations: We have the following system of equations: y = (7/9)x - (5/6) y = (9/4)x + (2/3) Identify whether the slopes of both the equations are the same. In y = (7/9)x - (5/6), the slope is 7/9. In y = (9/4)x + (2/3), the slope is 9/4. Since 7/9 is not equal to 9/4, the slopes of both equations are different.Comparison of slopes: Since the slopes are different, the lines represented by these equations are not parallel. This means they will intersect at some point. Therefore, the system of equations has a unique solution and is consistent.Intersection of lines: Because the system has a unique solution, the equations are independent of each other.

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Which describes the system of equations below? $\newline$ $y = \frac{7}{9}x - \frac{5}{6}$ $\newline$ $y = \frac{9}{4}x + \frac{2}{3}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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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{7}{9}x - \frac{5}{6}

\newline

y = \frac{9}{4}x + \frac{2}{3}

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Identify slopes of equations: We have the following system of equations: $\newline$ $y = \frac{7}{9}x - \frac{5}{6}$ $\newline$ $y = \frac{9}{4}x + \frac{2}{3}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = \frac{7}{9}x - \frac{5}{6}$ , the slope is $\frac{7}{9}$ . $\newline$ In $y = \frac{9}{4}x + \frac{2}{3}$ , the slope is $\frac{9}{4}$ . $\newline$ Since $\frac{7}{9}$ is not equal to $\frac{9}{4}$ , the slopes of both equations are different.
Comparison of slopes: 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 and is consistent.
Intersection of lines: Because the system has a unique solution, the equations are independent of each other.