https://file.aiquickdraw.com/mathbot/file/1729051805892961btk92.jpg

The image contains the following system of linear equations:

\[
\begin{cases}
2x_1 + x_2 = 8 \\
4x_1 - 3x_2 = 6
\end{cases}
\]

Let's solve this system using the substitution or elimination method. I'll use the elimination method here.

### Step 1: Make the coefficients of \( x_1 \) equal
We can multiply the first equation by 2 to match the coefficients of \( x_1 \):

\[
\begin{cases}
4x_1 + 2x_2 = 16 \\
4x_1 - 3x_2 = 6
\end{cases}
\]

### Step 2: Subtract the equations
Subtract the second equation from the first to eliminate \( x_1 \):

\[
(4x_1 + 2x_2) - (4x_1 - 3x_2) = 16 - 6
\]

\[
5x_2 = 10
\]

\[
x_2 = 2
\]

### Step 3: Substitute \( x_2 \) back into one of the original equations
Substitute \( x_2 = 2 \) into the first equation:

\[
2x_1 + 2 = 8
\]

\[
2x_1 = 6
\]

\[
x_1 = 3
\]

### Solution
The solution to the system is:

\[
x_1 = 3, \quad x_2 = 2
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Solve the system: \( 3x_1 + 4x_2 = 7 \) and \( 6x_1 - 8x_2 = -10 \).
2. What is the graphical interpretation of solving a system of two linear equations?
3. How can you check if a system of linear equations has no solution or infinitely many solutions?
4. Solve \( 5x_1 - 2x_2 = 12 \) and \( 7x_1 + 3x_2 = -1 \).
5. Can a system of two linear equations be solved using matrices? If yes, how?

**Tip:** When using the elimination method, ensure that the coefficients of one variable are made equal in both equations to easily eliminate that variable.

Solve the system of equations: 2x1 + x2 = 8 and 4x1 - 3x2 = 6

Explore how to solve a system of linear equations using the elimination method. This problem demonstrates key algebraic concepts for students in Grades 8-10, with a step-by-step solution for the equations 2x1 + x2 = 8 and 4x1 - 3x2 = 6.

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