How many solutions does the system of equations below have? y = 9x − 2 y = 9x + 4/3 Choices: (A)no solution (B)one solution (C)infinitely many solutions

Analyze slopes of equations: Step 1: Analyze the slopes of both equations. Equation 1: y = 9x - 2 (Slope = 9) Equation 2: y = 9x + 4/3 (Slope = 9) Both equations have the same slope. Compare y-intercepts: Step 2: Compare the y-intercepts of both equations. Equation 1: y = 9x - 2 (y-intercept = -2) Equation 2: y = 9x + 4/3 (y-intercept = 4/3) The y-intercepts are different. Determine number of solutions: Step 3: Determine the number of solutions. Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect. Therefore, there are no solutions to the system.

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How many solutions does the system of equations below have? $\newline$ $y = 9x - 2$ $\newline$ $y = 9x + \frac{4}{3}$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

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Math Problems

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 = 9x - 2

\newline

y = 9x + \frac{4}{3}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Analyze slopes of equations: Step $1$ : Analyze the slopes of both equations. $\newline$ Equation $1$ : $y = 9x - 2$ (Slope = $9$ ) $\newline$ Equation $2$ : $y = 9x + \frac{4}{3}$ (Slope = $9$ ) $\newline$ Both equations have the same slope.
Compare y-intercepts: Step $2$ : Compare the y-intercepts of both equations. $\newline$ Equation $1$ : $y = 9x - 2$ (y-intercept = $-2$ ) $\newline$ Equation $2$ : $y = 9x + \frac{4}{3}$ (y-intercept = $\frac{4}{3}$ ) $\newline$ The y-intercepts are different.
Determine number of solutions: Step $3$ : Determine the number of solutions. $\newline$ Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect. $\newline$ Therefore, there are no solutions to the system.