How many solutions does the system of equations below have? y = x − 5 y = –7/5x + 10/3 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of equations. We have two linear equations: 1) y = x − 5 2) y = –7/5x + 10/3 To find the number of solutions, we need to determine if the lines are parallel, the same line, or if they intersect at a single point.Compare Slopes: Compare the slopes of the two lines. The slope of the first equation is the coefficient of x, which is 1. The slope of the second equation is the coefficient of x, which is –7/5. Since the slopes are different (1 ≠ –7/5), the lines are not parallel and must intersect at exactly one point.Conclude Number of Solutions: Conclude the number of solutions. Because the lines are not parallel and have different slopes, they will intersect at exactly one point. Therefore, the system of equations has one solution.

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How many solutions does the system of equations below have? $\newline$ $y = x - 5$ $\newline$ $y = -\frac{7}{5}x + \frac{10}{3}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Q. How many solutions does the system of equations below have?

\newline

y = x - 5

\newline

y = -\frac{7}{5}x + \frac{10}{3}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of equations. $\newline$ We have two linear equations: $\newline$ $1$ ) $y = x - 5$ $\newline$ $2$ ) $y = -\frac{7}{5}x + \frac{10}{3}$ $\newline$ To find the number of solutions, we need to determine if the lines are parallel, the same line, or if they intersect at a single point.
Compare Slopes: Compare the slopes of the two lines. $\newline$ The slope of the first equation is the coefficient of $x$ , which is $1$ . $\newline$ The slope of the second equation is the coefficient of $x$ , which is $-\frac{7}{5}$ . $\newline$ Since the slopes are different ( $1 \neq -\frac{7}{5}$ ), the lines are not parallel and must intersect at exactly one point.
Conclude Number of Solutions: Conclude the number of solutions. $\newline$ Because the lines are not parallel and have different slopes, they will intersect at exactly one point. Therefore, the system of equations has $1$ solution.