How many solutions does the system of equations below have? y = –7x + 10 y = –7/4x − 7/4 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 = –7x + 10 y = –7/4x  −  7/4   Choices: (A)no solution (B)one solution (C)infinitely many solutions

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Analyze Equations: Analyze the given system of equations to determine the number of solutions. We have two equations: y = –7x + 10 (Equation 1) y = –7/4x – 7/4 (Equation 2) To find the number of solutions, we need to compare the slopes and y-intercepts of the two lines represented by these equations.Identify Parameters: Identify the slopes and y-intercepts of the two lines. For Equation 1, the slope (m1) is -7 and the y-intercept (b1) is 10. For Equation 2, the slope (m2) is -7/4 and the y-intercept (b2) is -7/4.Compare Slopes: Compare the slopes of the two lines. If the slopes are equal and the y-intercepts are different, the lines are parallel and there is no solution. If the slopes are equal and the y-intercepts are also equal, the lines coincide and there are infinitely many solutions. If the slopes are different, the lines intersect at one point and there is one solution.Determine Solutions: Determine the number of solutions based on the comparison. Since m1 = -7 and m2 = -7/4, the slopes are not equal. Therefore, the lines are not parallel and will intersect at one point.Conclude Solution: Conclude the number of solutions for the system of equations. Because the lines intersect at one point, there is exactly one solution to the system of equations.

How many solutions does the system of equations below have? $\newline$ $y = -7x + 10$ $\newline$ $y = -\frac{7}{4}x - \frac{7}{4}$ $\newline$ 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=−7x+10y = -7x + 10y=−7x+10\newliney=−74x−74y = -\frac{7}{4}x - \frac{7}{4}y=−47​x−47​\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

How many solutions does the system of equations below have? $\newline$ $y = -7x + 10$ $\newline$ $y = -\frac{7}{4}x - \frac{7}{4}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions