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We are given the following system of simultaneous equations:

1. \( 3y + x = 22 \)
2. \( x = y - 2 \)

### Step 1: Substitute \( x \) in terms of \( y \)

From the second equation, we have \( x = y - 2 \). We can substitute this into the first equation:

\[
3y + (y - 2) = 22
\]

### Step 2: Simplify the equation

Now simplify the equation:

\[
3y + y - 2 = 22
\]

Combine the \( y \) terms:

\[
4y - 2 = 22
\]

### Step 3: Solve for \( y \)

Add 2 to both sides:

\[
4y = 24
\]

Now divide by 4:

\[
y = 6
\]

### Step 4: Solve for \( x \)

Now that we have \( y = 6 \), substitute this into the second equation \( x = y - 2 \):

\[
x = 6 - 2 = 4
\]

### Final Answer:
The solution to the system of equations is:
\[
x = 4, \quad y = 6
\]

Would you like more details or have any further questions?

### Related Questions:
1. How can you verify if a solution satisfies a system of equations?
2. Can you solve this system graphically? How would the lines intersect?
3. What happens when two equations in a system have no solutions?
4. What if two equations in a system represent the same line?
5. How can you solve this system using matrices?

### Tip:
Always substitute your solution back into the original equations to verify that it's correct.

Solve the simultaneous equations below: 3y + x = 22 and x = y - 2

Learn how to solve the system of simultaneous equations 3y + x = 22 and x = y - 2 using the substitution method. This step-by-step solution demonstrates key algebraic concepts and is ideal for students in Grades 7-9.

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