How many solutions does the system of equations below have? y = –5/6x − 9 y = 5/3x + 5/2 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Slope Difference: System of equations: y = –5/6x – 9 y = 5/3x + 5/2 Are the slopes same or different? Slope of first equation: -5/6 Slope of second equation: 5/3 Slopes of the equations are different.Y-Intercept Difference: System of equations: y = –5/6x – 9 y = 5/3x + 5/2 Are the y-intercepts same or different? y-intercept of first equation: -9 y-intercept of second equation: 5/2 y-intercepts of the equations are different.Number of Solutions: System of equations: y = –5/6x – 9 y = 5/3x + 5/2 Determine the number of solutions to the system of equations. Since the slopes of the equations are different, the lines are not parallel and will intersect at one point. Therefore, the system of equations has one solution.

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How many solutions does the system of equations below have? $\newline$ $y = -\frac{5}{6}x - 9$ $\newline$ $y = \frac{5}{3}x + \frac{5}{2}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Algebra 1

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}{6}x - 9

\newline

y = \frac{5}{3}x + \frac{5}{2}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Slope Difference: System of equations: $\newline$ $y = -\frac{5}{6}x - 9$ $\newline$ $y = \frac{5}{3}x + \frac{5}{2}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $-\frac{5}{6}$ $\newline$ Slope of second equation: $\frac{5}{3}$ $\newline$ Slopes of the equations are different.
Y-Intercept Difference: System of equations: $\newline$ $y = -\frac{5}{6}x - 9$ $\newline$ $y = \frac{5}{3}x + \frac{5}{2}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $-9$ $\newline$ y-intercept of second equation: $\frac{5}{2}$ $\newline$ y-intercepts of the equations are different.
Number of Solutions: System of equations: $\newline$ $y = -\frac{5}{6}x - 9$ $\newline$ $y = \frac{5}{3}x + \frac{5}{2}$ $\newline$ Determine the number of solutions to the system of equations. $\newline$ Since the slopes of the equations are different, the lines are not parallel and will intersect at one point. $\newline$ Therefore, the system of equations has $1$ solution.