Question

1. here is a system of equations: $\begin{cases} x = 14 \\ 2x - 5y = 13 end{cases}$

in the solution $(x, y)$, what is the value of $y$

1. here is an incomplete system of equations. create a second equation so that the system has no solution.

$\begin{cases} y = \frac{3}{4}x - 4 \\ \boldsymbol{?} end{cases}$
spiral review

1. label each line on the graph with its corresponding equation.

• line a: $y = 2x + 3$
• line b: $y = -2x + 3$
• line c: $y = 2x - 3$
• line d: $y = -2x - 3$

Explanation:

Step1: Substitute $x=14$ into 2nd equation

$2(14) - 5y = 13$

Step2: Simplify left side

$28 - 5y = 13$

Step3: Isolate the $y$-term

$-5y = 13 - 28$
$-5y = -15$

Step4: Solve for $y$

$y = \frac{-15}{-5}$

Step1: Identify slope of given line

Given line: $y=\frac{3}{4}x - 4$, slope $m=\frac{3}{4}$

Step2: Write parallel line (no solution)

A line with same slope, different y-intercept, e.g., $y=\frac{3}{4}x + 1$

• Lines with positive slope ($2$) are upward-sloping: $y=2x+3$ (y-intercept $+3$, crosses y-axis at $(0,3)$) is the steeper upward line crossing the positive y-axis; $y=2x-3$ (y-intercept $-3$, crosses y-axis at $(0,-3)$) is the steeper upward line crossing the negative y-axis.
• Lines with negative slope ($-2$) are downward-sloping: $y=-2x+3$ (y-intercept $+3$, crosses y-axis at $(0,3)$) is the steeper downward line crossing the positive y-axis; $y=-2x-3$ (y-intercept $-3$, crosses y-axis at $(0,-3)$) is the steeper downward line crossing the negative y-axis.

Answer:

$y=3$

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