You provided the system of equations:

\[
\begin{aligned}
1. \, & 3X - 3Y = 18 \\
2. \, & X + 5Y = 18
\end{aligned}
\]

We can solve this system using either substitution or elimination. Let's proceed with the elimination method.

### Step 1: Simplify the first equation
Divide the first equation by 3 to make it simpler:

\[
X - Y = 6
\]

### Step 2: Solve for \(X\) in terms of \(Y\)
From the simplified first equation, we can express \(X\) in terms of \(Y\):

\[
X = Y + 6
\]

### Step 3: Substitute into the second equation
Now, substitute \(X = Y + 6\) into the second equation \(X + 5Y = 18\):

\[
(Y + 6) + 5Y = 18
\]

### Step 4: Solve for \(Y\)
Simplify the equation:

\[
Y + 6 + 5Y = 18 \\
6Y + 6 = 18 \\
6Y = 12 \\
Y = 2
\]

### Step 5: Solve for \(X\)
Now, substitute \(Y = 2\) back into the equation \(X = Y + 6\):

\[
X = 2 + 6 = 8
\]

### Final Solution:
The solution to the system of equations is:

\[
X = 8, \quad Y = 2
\]

Do you want more details or have any questions?

---

Here are 5 related questions to expand your understanding:

1. How do you solve a system of equations using the substitution method?
2. Can this system be solved graphically? What do the lines represent?
3. How would you solve the same system using the matrix method?
4. What happens if the system of equations has no solution?
5. What does it mean when a system has infinitely many solutions?

**Tip:** Always check your solution by substituting the values of \(X\) and \(Y\) back into the original equations to ensure they satisfy both.

This detailed solution walks through solving the system of linear equations 3X - 3Y = 18 and X + 5Y = 18 using the elimination and substitution methods. Learn algebraic concepts suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation