To solve this task, we need to identify the equations of the two lines in the graph, as the problem requires creating a system of linear equations from the graph.

Steps:

1. Identify the slope and y-intercept for each line.

   • Line 1: Find two points on the line and calculate the slope $m$ using $m = \frac{y_2 - y_1}{x_2 - x_1}$. Then, use the slope-intercept form $y = mx + b$ to find $b$.
   • Line 2: Repeat the process.

2. Confirm the intersection point.

   • The system of equations should reflect the given lines and their intersection point.

Let me analyze the image and extract the points to calculate the equations. PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/1732889656353n3kf4o3f.jpg" image = Image.open(image_path)

Use OCR to extract any visible text (not needed for calculations, but just in case)

extracted_text = pytesseract.image_to_string(image)

extracted_textThe OCR did not extract meaningful text. However, from the image, the points and slopes will be determined visually. Based on the graph:

1. Line 1:

   • Points: For this line, it appears to pass through $(-8, 8)$ and $(4, -4)$.
   • Slope: $m = \frac{-4 - 8}{4 - (-8)} = \frac{-12}{12} = -1$.
   • Equation: $y = -x + b$. Using one point $(-8, 8)$: $8 = -(-8) + b \implies 8 = 8 + b \implies b = 0$ So, the equation is $y = -x$.

2. Line 2:

   • Points: This line passes through $(-8, -4)$ and $(8, 4)$.
   • Slope: $m = \frac{4 - (-4)}{8 - (-8)} = \frac{8}{16} = \frac{1}{2}$.
   • Equation: $y = \frac{1}{2}x + b$. Using one point $(-8, -4)$: $-4 = \frac{1}{2}(-8) + b \implies -4 = -4 + b \implies b = 0$ So, the equation is $y = \frac{1}{2}x$.

System of Equations: