Which describes the system of equations below? y = 1/10x + 10/7 y = 1/10x + 10/7 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Compare slopes: We have the system of equations: y = (1/10)x + 10/7 y = (1/10)x + 10/7 First, we need to compare the slopes of both equations. In y = (1/10)x + 10/7, the slope is 1/10. In y = (1/10)x + 10/7, the slope is also 1/10. Since both slopes are equal, we can say that the lines are parallel or the same line.Compare y-intercepts: Next, we compare the y-intercepts of both equations. In y = (1/10)x + 10/7, the y-intercept is 10/7. In y = (1/10)x + 10/7, the y-intercept is also 10/7. Since both y-intercepts are equal, we can say that the lines have the same y-intercept.Determine line relationship: Since both the slope and y-intercept of the two equations are the same, the lines represented by these equations are the same line. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions. This makes the system consistent and dependent.

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Which describes the system of equations below? $\newline$ $y = \frac{1}{10}x + \frac{10}{7}$ $\newline$ $y = \frac{1}{10}x + \frac{10}{7}$ $\newline$ Choices: $\newline$ (A) inconsistent $\newline$ (B) consistent and independent $\newline$ (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{1}{10}x + \frac{10}{7}

\newline

y = \frac{1}{10}x + \frac{10}{7}

\newline

Choices:

\newline

(A) inconsistent

\newline

(B) consistent and independent

\newline

Compare slopes: We have the system of equations: $\newline$ y = $(\frac{1}{10})x + \frac{10}{7}$ $\newline$ y = $(\frac{1}{10})x + \frac{10}{7}$ $\newline$ First, we need to compare the slopes of both equations. $\newline$ In $y = (\frac{1}{10})x + \frac{10}{7}$ , the slope is $\frac{1}{10}$ . $\newline$ In $y = (\frac{1}{10})x + \frac{10}{7}$ , the slope is also $\frac{1}{10}$ . $\newline$ Since both slopes are equal, we can say that the lines are parallel or the same line.
Compare y-intercepts: Next, we compare the y-intercepts of both equations. $\newline$ In $y = \frac{1}{10}x + \frac{10}{7}$ , the y-intercept is $\frac{10}{7}$ . $\newline$ In $y = \frac{1}{10}x + \frac{10}{7}$ , the y-intercept is also $\frac{10}{7}$ . $\newline$ Since both y-intercepts are equal, we can say that the lines have the same y-intercept.
Determine line relationship: Since both the slope and $y$ -intercept of the two equations are the same, the lines represented by these equations are the same line. Therefore, every point on one line is also on the other line, which means the system has an infinite number of solutions. This makes the system consistent and dependent.