How many solutions does the system of equations below have? y = 2x + 10 y = –9/10x + 10/9 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations to determine if they are parallel, intersecting, or coincident. The first equation is y = 2x + 10, which is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. The slope of the first line is 2. The second equation is y = –9/10x + 10/9, which is also in slope-intercept form. The slope of the second line is –9/10. Since the slopes of the two lines are different (2 vs. –9/10), the lines are not parallel and must intersect at exactly one point.Determine Slopes: Since we have determined that the lines are not parallel, we can conclude that there is exactly one point of intersection. Therefore, the system of equations has one solution.

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How many solutions does the system of equations below have? $\newline$ $y = 2x + 10$ $\newline$ $y = -\frac{9}{10}x + \frac{10}{9}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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

\newline

y = 2x + 10

\newline

y = -\frac{9}{10}x + \frac{10}{9}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze Equations: Analyze the given system of linear equations to determine if they are parallel, intersecting, or coincident. $\newline$ The first equation is $y = 2x + 10$ , which is in slope-intercept form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. The slope of the first line is $2$ . $\newline$ The second equation is $y = -\frac{9}{10}x + \frac{10}{9}$ , which is also in slope-intercept form. The slope of the second line is $-\frac{9}{10}$ . $\newline$ Since the slopes of the two lines are different ( $2$ vs. $-\frac{9}{10}$ ), the lines are not parallel and must intersect at exactly one point.
Determine Slopes: Since we have determined that the lines are not parallel, we can conclude that there is exactly one point of intersection. Therefore, the system of equations has one solution.