How many solutions does the system of equations below have? y = 3x − 10 y = 9/10x − 4/5 Choices: (A)no solution (B)one solution (C)infinitely many solutions

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How many solutions does the system of equations below have?  y = 3x − 10 y = 9/10x  −  4/5   Choices: (A)no solution (B)one solution (C)infinitely many solutions

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Analyze Equations: Analyze the given system of linear equations to determine if they are the same line, parallel lines, or intersecting lines. The first equation is y = 3x − 10 and the second equation is y = 9/10x − 4/5. We can compare the slopes and y-intercepts of these two equations to determine the relationship between the lines they represent. The slope of the first equation is 3, and the y-intercept is -10. The slope of the second equation is 9/10, and the y-intercept is -4/5. Since the slopes are different (3 ≠ 9/10), the lines are not parallel and they are not the same line. Therefore, they must intersect at exactly one point.Compare Slopes and Intercepts: Solve the system of equations algebraically to find the point of intersection, which will confirm the number of solutions. We can set the two equations equal to each other since they both equal y: 3x − 10 = 9/10x − 4/5 To solve for x, we can multiply both sides of the equation by 10 to eliminate the fractions: 10(3x − 10) = 10(9/10x − 4/5) 30x − 100 = 9x − 8 Now, we can subtract 9x from both sides to get: 30x − 9x − 100 = −8 21x − 100 = −8 Next, we add 100 to both sides to isolate the term with x: 21x = 92 Finally, we divide both sides by 21 to solve for x: x = 92/21 Since we found a unique solution for x, and we can substitute this back into either of the original equations to find the corresponding y value, this confirms that there is exactly one solution to the system of equations.

How many solutions does the system of equations below have? $\newline$ $y = 3x - 10$ $\newline$ $y = \frac{9}{10}x - \frac{4}{5}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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How many solutions does the system of equations below have?\newliney=3x−10y = 3x - 10y=3x−10\newliney=910x−45y = \frac{9}{10}x - \frac{4}{5}y=109​x−54​\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

How many solutions does the system of equations below have? $\newline$ $y = 3x - 10$ $\newline$ $y = \frac{9}{10}x - \frac{4}{5}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions