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How many solutions does the system of equations below have? $\newline$ $y = \frac{5}{7}x + \frac{3}{4}$ $\newline$ $y = \frac{5}{7}x - \frac{2}{7}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Find the number of solutions to a system of equations

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

\newline

y = \frac{5}{7}x + \frac{3}{4}

\newline

y = \frac{5}{7}x - \frac{2}{7}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Slope Analysis: System of equations: $\newline$ $y = \frac{5}{7}x + \frac{3}{4}$ $\newline$ $y = \frac{5}{7}x - \frac{2}{7}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $\frac{5}{7}$ $\newline$ Slope of second equation: $\frac{5}{7}$ $\newline$ Slopes of the equations are the same.
Y-Intercept Comparison: System of equations: $\newline$ $y = \frac{5}{7}x + \frac{3}{4}$ $\newline$ $y = \frac{5}{7}x - \frac{2}{7}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $\frac{3}{4}$ $\newline$ y-intercept of second equation: $-\frac{2}{7}$ $\newline$ y-intercepts of the equations are different.
Number of Solutions: System of equations: $\newline$ $y = \frac{5}{7}x + \frac{3}{4}$ $\newline$ $y = \frac{5}{7}x - \frac{2}{7}$ $\newline$ Determine the number of solutions to the system of equations. $\newline$ The system of equations has the same slope but different y-intercepts. $\newline$ The system of equations has no solution because they are parallel lines.

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