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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.

In Exercises 21 and 22, write and solve a system of linear equations to find the values of x and y.

This problem involves solving systems of linear equations by applying geometric concepts such as vertically opposite angles and the properties of trapezoids. Suitable for students in Grades 8-10, it demonstrates how algebra and geometry intersect in solving real-world problems.

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