can you help solve this linear equation x + y = 3  3x - 2y = 4

Yes, let's solve the system of linear equations:

\[
\begin{align*}
1. & \quad x + y = 3 \\
2. & \quad 3x - 2y = 4
\end{align*}
\]

### Step 1: Solve the first equation for \( x \) or \( y \).

From the first equation \( x + y = 3 \), solve for \( x \):

\[
x = 3 - y
\]

### Step 2: Substitute \( x \) into the second equation.

Substitute \( x = 3 - y \) into the second equation \( 3x - 2y = 4 \):

\[
3(3 - y) - 2y = 4
\]

Simplify the equation:

\[
9 - 3y - 2y = 4
\]
\[
9 - 5y = 4
\]

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

Subtract 9 from both sides:

\[
-5y = 4 - 9
\]
\[
-5y = -5
\]

Now, divide by \(-5\):

\[
y = 1
\]

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

Substitute \( y = 1 \) back into the equation \( x = 3 - y \):

\[
x = 3 - 1
\]
\[
x = 2
\]

### Solution:

The solution to the system is:

\[
x = 2, \quad y = 1
\]

Would you like more details on the steps or have any questions?

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Here are 5 questions to expand your understanding:

1. How can you verify if the solution \(x = 2, y = 1\) is correct?
2. Can you solve the system using substitution for \( y \) instead of \( x \)?
3. How would you graph these two equations and find their point of intersection?
4. What is the general method to solve a system using the elimination technique?
5. How would the solution change if the second equation were \(3x + 2y = 4\)?

**Tip:** Always check your solutions by substituting the values back into both original equations.

Learn how to solve the system of linear equations x + y = 3 and 3x - 2y = 4 using the substitution method. This detailed step-by-step solution covers key algebraic concepts, including substitution and simplification, and is suitable for students in Grades 8-10.

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