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

Compare Equations: We are given the system of equations: y = –x − 10 y = –x − 10 First, we need to compare the two equations to determine if they are the same or different. Identical Equations: Upon inspection, we can see that both equations are identical: Equation 1: y = –x − 10 Equation 2: y = –x − 10 This means that every solution to the first equation is also a solution to the second equation. Same Line on Graph: Since both equations are the same, they represent the same line on a graph. Therefore, the system has infinitely many solutions where the two lines would overlap completely. Consistent and Dependent System: A system of equations with infinitely many solutions is known as a consistent and dependent system. This is because the equations are consistent (they have at least one solution) and dependent (they are essentially the same line, so all solutions of one are solutions of the other).

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Which describes the system of equations below? $\newline$ $y = -x - 10$ $\newline$ $y = -x - 10$ $\newline$ 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 = -x - 10

\newline

y = -x - 10

\newline

Choices:

\newline

(A)inconsistent

\newline

(B)consistent and independent

\newline

(C)consistent and dependent

Compare Equations: We are given the system of equations: $\newline$ $y = -x - 10$ $\newline$ $y = -x - 10$ $\newline$ First, we need to compare the two equations to determine if they are the same or different.
Identical Equations: Upon inspection, we can see that both equations are identical: $\newline$ Equation $1$ : $y = -x - 10$ $\newline$ Equation $2$ : $y = -x - 10$ $\newline$ This means that every solution to the first equation is also a solution to the second equation.
Same Line on Graph: Since both equations are the same, they represent the same line on a graph. Therefore, the system has infinitely many solutions where the two lines would overlap completely.
Consistent and Dependent System: A system of equations with infinitely many solutions is known as a consistent and dependent system. This is because the equations are consistent (they have at least one solution) and dependent (they are essentially the same line, so all solutions of one are solutions of the other).