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How many solutions does the system of equations below have? $\newline$ $y = -\frac{9}{5}x + 7$ $\newline$ $y = -\frac{9}{5}x + \frac{10}{9}$ $\newline$ 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

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

\newline

y = -\frac{9}{5}x + 7

\newline

y = -\frac{9}{5}x + \frac{10}{9}

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Slope Analysis: System of equations: $\newline$ $y = \frac{-9}{5}x + 7$ $\newline$ $y = \frac{-9}{5}x + \frac{10}{9}$ $\newline$ Are the slopes same or different? $\newline$ Slope of first equation: $-\frac{9}{5}$ $\newline$ Slope of second equation: $-\frac{9}{5}$ $\newline$ Slopes of the equations are the same.
Y-Intercept Comparison: System of equations: $\newline$ $y = -\frac{9}{5}x + 7$ $\newline$ $y = -\frac{9}{5}x + \frac{10}{9}$ $\newline$ Are the y-intercepts same or different? $\newline$ y-intercept of first equation: $7$ $\newline$ y-intercept of second equation: $\frac{10}{9}$ $\newline$ y-intercepts of the equations are different.
Number of Solutions: System of equations: $\newline$ $y = -\frac{9}{5}x + 7$ $\newline$ $y = -\frac{9}{5}x + \frac{10}{9}$ $\newline$ Determine the number of solutions to the system of equations. $\newline$ The system of equations has the same slope but different y-intercepts. $\newline$ The system of equations has no solution.

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Jessie tried to solve an equation step by step.

\newline

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Find Jessie's mistake.

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Leon tried to solve an equation step by step.

\newline

\begin{aligned} \frac{1}{2} w-12 & =18 \\ \frac{1}{2} w & =30 \quad \text { Step } 1 \\ w & =15 \quad \text { Step 2 } \end{aligned}

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Find Leon's mistake.

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\newline

\begin{array}{rlrl} \frac{1}{4}\left(\frac{1}{3} k+9\right) & =6 & \\ \frac{1}{3} k+9 & =24 \quad \text { Step 1 } \\ \frac{1}{3} k & =15 \quad \text { Step 2 } \\ k & =5 \quad \text { Step 3 } \end{array}

\newline

Find Olga's mistake.

\newline

1

\newline

1

\newline

2

\newline

\operatorname{Step} 3

\newline

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\newline

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\newline

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\newline

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Question

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\newline

1

\newline

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4

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(D) The limit doesn't exist

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