The image contains two problems, numbered 21 and 22. Both require writing and solving a system of linear equations to find the values of $x$ and $y$.

Problem 21:

This problem involves angles formed by intersecting lines.

You are given:

• One angle marked as $3x$.
• Two angles marked as $2x + 30^\circ$.
• Two angles marked as $90^\circ - 10y$.

Using the properties of angles formed by intersecting lines, such as the fact that vertically opposite angles are equal and the sum of angles on a straight line is $180^\circ$, we can set up the following equations:

1. $3x = 2x + 30^\circ$
2. $3x + (90^\circ - 10y) = 180^\circ$

Problem 22:

This problem involves a trapezoid with given angles.

You are given:

• Two angles marked as $2x + 12^\circ$ and $3y + 6^\circ$.
• The angles opposite to them are marked as $2x$ and $y + 6^\circ$.

Since the sum of the angles in a trapezoid is $360^\circ$ and adjacent angles are supplementary (sum to $180^\circ$), you can set up the following equations:

1. $(2x + 12^\circ) + 2x = 180^\circ$
2. $(3y + 6^\circ) + (y + 6^\circ) = 180^\circ$

Would you like to see the detailed solution for these equations?

Questions to Consider:

1. How do you solve a system of linear equations with two variables?
2. What is the significance of vertically opposite angles in solving Problem 21?
3. How can you verify the solution of a system of linear equations?
4. What is the role of supplementary angles in Problem 22?
5. How does the trapezoid's properties influence the setup of the equations in Problem 22?

Tip:

Remember that when dealing with geometric figures, the sum of angles is crucial in setting up equations that represent the problem accurately.