Question

solving systems using substitution: practice

choose the system of equations represented by the graph:

option 1:
\\(\

$$\begin{cases} y = 2x - 1 \\\\ y = -2x - 1 \\end{cases}$$

\\)

option 2:
\\(\

$$\begin{cases} y = -2x + 1 \\\\ y = 2x + 1 \\end{cases}$$

\\)

option 3:
\\(\

$$\begin{cases} y = -2x - 1 \\\\ y = 2x + 1 \\end{cases}$$

\\)

option 4:
\\(\

$$\begin{cases} y = 2x + 1 \\\\ y = 2x - 1 \\end{cases}$$

\\)

Explanation:

⚡ Using what you learned: solving systems by graphing

Step 1: Identify the y-intercepts

Blue line:

$$ y\text{-intercept} = (0, 1) \implies b_1 = 1 $$

Red line:

$$ y\text{-intercept} = (0, -1) \implies b_2 = -1 $$

Step 2: Determine the slopes

Both lines are parallel and rise \( 2 \) units for every \( 1 \) unit they move to the right:

$$ m = \frac{\text{rise}}{\text{run}} = \frac{2}{1} = 2 $$

Step 3: Write the system of equations

Using slope-intercept form \( y = mx + b \):

Blue line:

$$ y = 2x + 1 $$

Red line:

$$ y = 2x - 1 $$

Answer:

$$
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$$