Which describes the system of equations below? y = 3x − 4 y = 3x + 8/7 Choices: (A)consistent and independent (B)inconsistent (C)consistent and dependent

Slope Comparison: We have the following system of equations: y = 3x − 4 y = 3x + 8/7 Identify whether the slopes of both the equations are the same. In y = 3x − 4, the slope is 3. In y = 3x + 8/7, the slope is also 3. Yes, the slopes of both equations are the same.Y-Intercept Comparison: Now, identify whether the y-intercepts of both the equations are the same. In y = 3x − 4, the y-intercept is -4. In y = 3x + 8/7, the y-intercept is 8/7. No, the y-intercepts of both equations are not the same.Conclusion: Since the slopes of the equations are the same but the y-intercepts are different, the lines are parallel to each other and do not intersect. This means that there are no solutions where both equations are satisfied simultaneously. Therefore, the system of equations is inconsistent.

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Which describes the system of equations below? $\newline$ $y = 3x - 4$ $\newline$ $y = 3x + \frac{8}{7}$ $\newline$ Choices: $\newline$ (A)consistent and independent $\newline$ (B)inconsistent $\newline$ (C)consistent and dependent

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Math Problems

Algebra 1

Classify a system of equations

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Q. Which describes the system of equations below?

\newline

y = 3x - 4

\newline

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

\newline

Choices:

\newline

(A)consistent and independent

\newline

(B)inconsistent

\newline

(C)consistent and dependent

Slope Comparison: We have the following system of equations: $\newline$ $y = 3x − 4$ $\newline$ $y = 3x + \frac{8}{7}$ $\newline$ Identify whether the slopes of both the equations are the same. $\newline$ In $y = 3x − 4$ , the slope is $3$ . $\newline$ In $y = 3x + \frac{8}{7}$ , the slope is also $3$ . $\newline$ Yes, the slopes of both equations are the same.
Y-Intercept Comparison: Now, identify whether the y-intercepts of both the equations are the same. $\newline$ In $y = 3x − 4$ , the y-intercept is $-4$ . $\newline$ In $y = 3x + \frac{8}{7}$ , the y-intercept is $\frac{8}{7}$ . $\newline$ No, the y-intercepts of both equations are not the same.
Conclusion: Since the slopes of the equations are the same but the $y$ -intercepts are different, the lines are parallel to each other and do not intersect. $\newline$ This means that there are no solutions where both equations are satisfied simultaneously. $\newline$ Therefore, the system of equations is inconsistent.