Let me analyze the image and provide a solution for the given problem.

I'll first extract the mathematical content from the image and proceed with the requested tasks. PIL import Image

Open and display the uploaded image to extract its contents

img_path = '/mnt/data/1739656676039qa3cusat.jpg' img = Image.open(img_path) img.show()I have displayed the image. Now, I will proceed by extracting the details and solving the questions provided. Please give me a moment to work through them.Based on the problem in the image, here’s how we can proceed:

Part a) - Create an equation equivalent to $x + y = 3$

To create an equivalent equation, we can solve for one variable in terms of the other. Let’s solve for $y$ in terms of $x$:

$x + y = 3$

Subtract $x$ from both sides:

$y = 3 - x$

This is the equivalent equation to $x + y = 3$.

Part b) - Solve the simultaneous equations:

We are given the system of equations:

1. $2x + 3y = 7$
2. $x + y = 3$ (from part a, we already know that $y = 3 - x$)

Now, substitute $y = 3 - x$ into the first equation:

$2x + 3(3 - x) = 7$

Simplify and solve for $x$:

$2x + 9 - 3x = 7$ $-x + 9 = 7$ $-x = 7 - 9$ $-x = -2$ $x = 2$

Now substitute $x = 2$ into $y = 3 - x$:

$y = 3 - 2 = 1$

Solution:

The solution to the system of simultaneous equations is: $x = 2, \quad y = 1$

If you have any questions or would like further details, feel free to ask!

Additional Questions:

1. How can we check the solution to the system of equations?
2. What would happen if we used substitution in reverse order?
3. How do you solve simultaneous equations when they are nonlinear?
4. Can these equations be represented graphically? What would the graphs look like?
5. What other methods can be used to solve systems of linear equations?

Tip: For simultaneous equations, substitution is often useful when one equation is already solved for one variable.