Which describes the system of equations below? y = 10x + 2 y = 3/7x + 8/3 Choices: (A)inconsistent (B)consistent and dependent (C)consistent and independent

Identify slopes of equations: We have the following system of equations: y = 10x + 2 y = (3/7)x + (8/3) Identify whether the slopes of both the equations are the same. In y = 10x + 2, the slope is 10. In y = (3/7)x + (8/3), the slope is 3/7. No, the slopes of both the equations are not the same.Determine intersection point: Since the slopes are different, the lines are not parallel and will intersect at exactly one point. This means the system of equations has one solution where the two lines intersect. Therefore, the system of equations is consistent and independent.Choose correct description: Choose the option which describes the given system of equations. Since the system has one solution and the lines are not the same or parallel, the correct choice is: (C) consistent and independent.

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Which describes the system of equations below? $\newline$ $y = 10x + 2$ $\newline$ $y = \frac{3}{7}x + \frac{8}{3}$ $\newline$ Choices: $\newline$ (A)inconsistent $\newline$ (B)consistent and dependent $\newline$ (C)consistent and independent

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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 = 10x + 2

\newline

y = \frac{3}{7}x + \frac{8}{3}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and dependent

\newline

(C)consistent and independent

Identify slopes of equations: We have the following system of equations: $\newline$ $y = 10x + 2$ $\newline$ $y = \frac{3}{7}x + \frac{8}{3}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 10x + 2$ , the slope is $10$ . $\newline$ In $y = \frac{3}{7}x + \frac{8}{3}$ , the slope is $\frac{3}{7}$ . $\newline$ No, the slopes of both the equations are not the same.
Determine intersection point: Since the slopes are different, the lines are not parallel and will intersect at exactly one point. This means the system of equations has one solution where the two lines intersect. Therefore, the system of equations is consistent and independent.
Choose correct description: Choose the option which describes the given system of equations. $\newline$ Since the system has one solution and the lines are not the same or parallel, the correct choice is: $\newline$ (C) consistent and independent.