Which describes the system of equations below? y = 9x − 2 y = 9x + 10/9 Choices: (A)inconsistent (B)consistent and independent (C)consistent and dependent

Analyze slopes: Step 1: Analyze the slopes of both equations. - Equation 1: y = 9x − 2, slope = 9. - Equation 2: y = 9x + 10/9, slope = 9. Both equations have the same slope. Compare y-intercepts: Step 2: Compare the y-intercepts of both equations. - Equation 1: y = 9x − 2, y-intercept = -2. - Equation 2: y = 9x + 10/9, y-intercept = 10/9. The y-intercepts are different. Determine system type: Step 3: Determine the type of system based on slopes and y-intercepts. Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect. This means the system has no solution.

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Which describes the system of equations below? $\newline$ $y = 9x - 2$ $\newline$ $y = 9x + \frac{10}{9}$ $\newline$ 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 = 9x - 2

\newline

y = 9x + \frac{10}{9}

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Analyze slopes: Step $1$ : Analyze the slopes of both equations. $\newline$ - Equation $1$ : $y = 9x − 2$ , slope = $9$ . $\newline$ - Equation $2$ : $y = 9x + \frac{10}{9}$ , slope = $9$ . $\newline$ Both equations have the same slope.
Compare y-intercepts: Step $2$ : Compare the y-intercepts of both equations. $\newline$ - Equation $1$ : $y = 9x − 2$ , y-intercept = $-2$ . $\newline$ - Equation $2$ : $y = 9x + \frac{10}{9}$ , y-intercept = $\frac{10}{9}$ . $\newline$ The y-intercepts are different.
Determine system type: Step $3$ : Determine the type of system based on slopes and y-intercepts. $\newline$ Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect. This means the system has no solution.