How many solutions does the system of equations below have? y = 1/2x − 2/3 y = –2/7x + 4/9 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Slopes: Analyze the slopes of both equations. The slope of the first equation (y = 1/2x - 2/3) is 1/2. The slope of the second equation (y = –2/7x + 4/9) is –2/7. Since the slopes are different, the lines are not parallel.Different Slopes: Since the slopes are different, the lines will intersect at exactly one point. This means there is one unique solution to the system of equations.Unique Solution: There is no need to find the exact point of intersection since we are only asked about the number of solutions. We have determined that there is one unique solution because the lines have different slopes and will intersect at one point.

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How many solutions does the system of equations below have? $\newline$ $y = \frac{1}{2}x - \frac{2}{3}$ $\newline$ $y = -\frac{2}{7}x + \frac{4}{9}$ $\newline$ 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{1}{2}x - \frac{2}{3}

\newline

y = -\frac{2}{7}x + \frac{4}{9}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Slopes: Analyze the slopes of both equations. $\newline$ The slope of the first equation $y = \frac{1}{2}x - \frac{2}{3}$ is $\frac{1}{2}$ . $\newline$ The slope of the second equation $y = -\frac{2}{7}x + \frac{4}{9}$ is $-\frac{2}{7}$ . $\newline$ Since the slopes are different, the lines are not parallel.
Different Slopes: Since the slopes are different, the lines will intersect at exactly one point. $\newline$ This means there is one unique solution to the system of equations.
Unique Solution: There is no need to find the exact point of intersection since we are only asked about the number of solutions. We have determined that there is one unique solution because the lines have different slopes and will intersect at one point.