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How many solutions does the system of equations below have? $\newline$ $y = -7x - 6$ $\newline$ $y = \frac{2}{9}x + \frac{8}{5}$ $\newline$ 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

Full solution

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

\newline

y = -7x - 6

\newline

y = \frac{2}{9}x + \frac{8}{5}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze slopes: Analyze the slopes of the two equations. $\newline$ The slope of the first equation $y = -7x - 6$ is $-7$ . $\newline$ The slope of the second equation $y = \frac{2}{9}x + \frac{8}{5}$ is $\frac{2}{9}$ . $\newline$ 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. 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 because the question only asks for the number of solutions, not the solution itself.

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