We have the following system of linear equations:

1. \( 2x + 3y + 3z = 90 \)
2. \( y - 3z = 20 \)

Let's solve this system step by step.

### Step 1: Solve the second equation for \( y \)
From the second equation:
\[
y = 3z + 20
\]

### Step 2: Substitute \( y = 3z + 20 \) into the first equation
Substitute this expression for \( y \) into the first equation:
\[
2x + 3(3z + 20) + 3z = 90
\]
Simplify:
\[
2x + 9z + 60 + 3z = 90
\]
Combine like terms:
\[
2x + 12z + 60 = 90
\]
Subtract 60 from both sides:
\[
2x + 12z = 30
\]
Divide the whole equation by 2:
\[
x + 6z = 15
\]
Now, we have the simplified equation:
\[
x = 15 - 6z
\]

### Step 3: Express \( x \) and \( y \) in terms of \( z \)
- \( x = 15 - 6z \)
- \( y = 3z + 20 \)

Thus, the general solution for this system is expressed in terms of \( z \), which can take any real value.

Would you like more details or have any questions?

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Here are five related questions:

1. What happens if \( z = 0 \)? What values of \( x \) and \( y \) do we get?
2. Can this system be solved using matrix methods such as Gaussian elimination?
3. What geometric interpretation can we give for this system of equations?
4. How would the solution change if the first equation was \( 2x + 3y + 3z = 100 \) instead of 90?
5. Could we use substitution or elimination methods for solving larger systems of equations?

**Tip:** When solving systems of linear equations, try to isolate one variable first to simplify the problem.

Solve the following system of linear equations: 2x + 3y + 3z = 90, y - 3z = 20

Learn how to solve a system of linear equations involving three variables. This guide walks through the step-by-step solution of the equations 2x + 3y + 3z = 90 and y - 3z = 20 using substitution methods. Understand the algebraic concepts and methods involved, suitable for students in Grades 9-12.

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