Let's analyze and solve the questions from the uploaded image step-by-step. I'll begin with the first question. Let me know which question you'd like me to solve first or if you prefer detailed solutions for all of them.

Question 1.2

Solve for $x$ and $y$ simultaneously in the equations:

1. $3x - y = 6$
2. $x^2 - 3x + xy - y = 22$

We will solve this step-by-step.

Step 1: Solve $3x - y = 6$ for $y$:

$y = 3x - 6$

Step 2: Substitute $y = 3x - 6$ into the second equation:

$x^2 - 3x + x(3x - 6) - (3x - 6) = 22$

Simplify: $x^2 - 3x + 3x^2 - 6x - 3x + 6 = 22$

$4x^2 - 12x + 6 = 22$

$4x^2 - 12x - 16 = 0$

Step 3: Simplify the quadratic equation:

$x^2 - 3x - 4 = 0$

Factorize: $(x - 4)(x + 1) = 0$

So: $x = 4 \quad \text{or} \quad x = -1$

Step 4: Solve for $y$ using $y = 3x - 6$:

1. If $x = 4$: $y = 3(4) - 6 = 12 - 6 = 6$

2. If $x = -1$: $y = 3(-1) - 6 = -3 - 6 = -9$

Final Solutions:

$(x, y) = (4, 6) \quad \text{or} \quad (x, y) = (-1, -9)$

Would you like me to move on to Question 1.3 or any other part of this question?
Here are 5 related questions that expand on the solution above:

1. What are the conditions for a quadratic equation to have real solutions?
2. How can substitution be used in solving non-linear systems of equations?
3. What happens if a system of equations has no solutions?
4. How would the solution change if the second equation were $x^2 + 3x + xy - y = 22$?
5. What is the graphical interpretation of solving $3x - y = 6$ and $x^2 - 3x + xy - y = 22$?

Tip: Always simplify one equation to express one variable in terms of another for substitution.