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

Analyze first equation: Analyze the first equation. The first equation is y = 7x − 7. This is a linear equation with a slope of 7 and a y-intercept of -7.Analyze second equation: Analyze the second equation. The second equation is y = 8/5x + 8/5. This is also a linear equation with a slope of 8/5 and a y-intercept of 8/5.Compare slopes: Compare the slopes of the two equations. The slope of the first equation is 7, and the slope of the second equation is 8/5. Since 7 is not equal to 8/5, the slopes are different.Determine solutions: Determine the number of solutions. Since the two lines have different slopes, they 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? $\newline$ $y = 7x - 7$ $\newline$ $y = \frac{8}{5}x + \frac{8}{5}$ $\newline$ 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 = 7x - 7

\newline

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

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze first equation: Analyze the first equation. $\newline$ The first equation is $y = 7x − 7$ . This is a linear equation with a slope of $7$ and a $y$ -intercept of $-7$ .
Analyze second equation: Analyze the second equation. $\newline$ The second equation is $y = \frac{8}{5}x + \frac{8}{5}$ . This is also a linear equation with a slope of $\frac{8}{5}$ and a y-intercept of $\frac{8}{5}$ .
Compare slopes: Compare the slopes of the two equations. $\newline$ The slope of the first equation is $7$ , and the slope of the second equation is $\frac{8}{5}$ . Since $7$ is not equal to $\frac{8}{5}$ , the slopes are different.
Determine solutions: Determine the number of solutions. $\newline$ Since the two lines have different slopes, they will intersect at exactly one point. Therefore, the system of equations has $1$ solution.