How many solutions does the system of equations below have? y = 2x − 2/5 y = 8/7x + 8/5 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Write Equations: Write down the given system of equations. y = 2x − 2/5 y = 8/7x + 8/5Compare Slopes: To find the number of solutions, we need to check if the two lines represented by the equations are the same line (infinitely many solutions), parallel (no solution), or intersect at one point (one solution). We can compare the slopes of the lines to determine this. The slope of the first line is 2, and the slope of the second line is 8/7. Since 2 is not equal to 8/7, the lines are not parallel and they are not the same line.Determine Number of Solutions: Because the slopes are different, the lines 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? $\newline$ $y = 2x - \frac{2}{5}$ $\newline$ $y = \frac{8}{7}x + \frac{8}{5}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions $\newline$

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

\newline

y = 2x - \frac{2}{5}

\newline

y = \frac{8}{7}x + \frac{8}{5}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

\newline

Write Equations: Write down the given system of equations. $\newline$ $y = 2x - \frac{2}{5}$ $\newline$ $y = \frac{8}{7}x + \frac{8}{5}$
Compare Slopes: To find the number of solutions, we need to check if the two lines represented by the equations are the same line (infinitely many solutions), parallel (no solution), or intersect at one point (one solution). We can compare the slopes of the lines to determine this. $\newline$ The slope of the first line is $2$ , and the slope of the second line is $\frac{8}{7}$ . Since $2 \neq \frac{8}{7}$ , the lines are not parallel and they are not the same line.
Determine Number of Solutions: Because the slopes are different, the lines will intersect at exactly one point. Therefore, the system of equations has $1$ solution.