Which describes the system of equations below? y = 4x + 6 y = –10/7x + 5/7 Choices: (A)consistent and dependent (B)inconsistent (C)consistent and independent

Analyze slopes: Step 1: Analyze the slopes of both equations. For y = 4x + 6, the slope is 4. For y = -10/7x + 5/7, the slope is -10/7. Since the slopes are different, the lines are not parallel. Check intersection: Step 2: Check if the lines intersect. Different slopes imply that the lines will intersect at exactly one point. This means the system has one solution. Determine system type: Step 3: Determine the type of system based on the number of solutions. Since there is exactly one solution, the system is consistent. Also, because they intersect at only one point, the equations are independent.

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Which describes the system of equations below? $\newline$ $y = 4x + 6$ $\newline$ $y = -\frac{10}{7}x + \frac{5}{7}$ $\newline$ Choices: $\newline$ (A)consistent and dependent $\newline$ (B)inconsistent $\newline$ (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 = 4x + 6

\newline

y = -\frac{10}{7}x + \frac{5}{7}

\newline

Choices:

\newline

(A)consistent and dependent

\newline

(B)inconsistent

\newline

(C)consistent and independent

Analyze slopes: Step $1$ : Analyze the slopes of both equations. $\newline$ For $y = 4x + 6$ , the slope is $4$ . $\newline$ For $y = -\frac{10}{7}x + \frac{5}{7}$ , the slope is $-\frac{10}{7}$ . $\newline$ Since the slopes are different, the lines are not parallel.
Check intersection: Step $2$ : Check if the lines intersect. $\newline$ Different slopes imply that the lines will intersect at exactly one point. $\newline$ This means the system has one solution.
Determine system type: Step $3$ : Determine the type of system based on the number of solutions. Since there is exactly one solution, the system is consistent. Also, because they intersect at only one point, the equations are independent.