from PIL import Image import pytesseract

Load the image to extract text

image_path = '/mnt/data/1732501454290pc2lnw1j.jpg' extracted_text = pytesseract.image_to_string(Image.open(image_path))

extracted_text'y=r—Sr+5\ny=5r—20\n''y=r—Sr+5\ny=5r—20\n'successThe equations extracted from the image are:

1. $y = x^2 - 5x + 5$
2. $y = 5x - 20$

Solving by substitution:

Since $y$ is equal in both equations, we can set the right-hand sides of the equations equal to each other:

$x^2 - 5x + 5 = 5x - 20$

Simplify the equation:

$x^2 - 5x - 5x + 5 + 20 = 0$ $x^2 - 10x + 25 = 0$

Factorize the quadratic equation:

$(x - 5)(x - 5) = 0$

So, $x = 5$ (a repeated root).

Find $y$ using $y = 5x - 20$:

$y = 5(5) - 20 = 25 - 20 = 5$

Solution:

The point of intersection is: $(x, y) = (5, 5)$

Would you like a detailed step-by-step explanation or graphical representation of this? Here are some related questions:

1. How do you verify the solution of a substitution problem?
2. What happens if the equations describe parallel lines?
3. Can you explain substitution in a system with more variables?
4. How can we graphically confirm the solution?
5. What if the quadratic equation had two distinct roots?

Tip: Always double-check your solution by substituting back into the original equations.