How many solutions does the system of equations below have? y = –2x + 9/4 y = –2x + 4/5 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Slope Analysis: System of equations: y = –2x + 9/4 y = –2x + 4/5 Are the slopes same or different? Slope of first equation: -2 Slope of second equation: -2 Slopes of the equations are the same.Y-Intercept Comparison: System of equations: y = –2x + 9/4 y = –2x + 4/5 Are the y-intercepts same or different? y-intercept of first equation: 9/4 y-intercept of second equation: 4/5 y-intercepts of the equations are different.Solution Determination: System of equations: y = –2x + 9/4 y = –2x + 4/5 Determine the number of solutions to the system of equations. The system of equations has the same slope but different y-intercepts. The system of equations has no solution because they are parallel lines that never intersect.

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How many solutions does the system of equations below have? $\newline$ $y = -2x + \frac{9}{4}$ $\newline$ $y = -2x + \frac{4}{5}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Math Problems

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 = -2x + \frac{9}{4}

\newline

y = -2x + \frac{4}{5}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Slope Analysis: System of equations: $\newline$ $y = -2x + \frac{9}{4}$ $\newline$ $y = -2x + \frac{4}{5}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $-2$ $\newline$ Slope of second equation: $-2$ $\newline$ Slopes of the equations are the same.
Y-Intercept Comparison: System of equations: $\newline$ $y = -2x + \frac{9}{4}$ $\newline$ $y = -2x + \frac{4}{5}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $\frac{9}{4}$ $\newline$ y-intercept of second equation: $\frac{4}{5}$ $\newline$ y-intercepts of the equations are different.
Solution Determination: System of equations: $\newline$ $y = -2x + \frac{9}{4}$ $\newline$ $y = -2x + \frac{4}{5}$ $\newline$ 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 that never intersect.