## Solving Systems of Linear Equations

This article will guide you through the process of solving a system of linear equations. We will be working with the following system:

**Equation 1:** (x + 2) / 7 + x / 4 = 2x - 8

**Equation 2:** (2y - 3x) / 3 + 2y = 3x + 4

### Step 1: Simplify the Equations

**For Equation 1:**

**Find a common denominator:**Multiply the first term by 4/4 and the second term by 7/7. This gives us: (4(x + 2)) / 28 + (7x) / 28 = 2x - 8**Combine the terms on the left side:**(4x + 8 + 7x) / 28 = 2x - 8 (11x + 8) / 28 = 2x - 8**Multiply both sides by 28:**11x + 8 = 56x - 224**Simplify:**-45x = -232

**For Equation 2:**

**Multiply both sides by 3:**2y - 3x + 6y = 9x + 12**Combine like terms:**8y - 3x = 9x + 12**Simplify:**8y = 12x + 12

### Step 2: Solve for One Variable

**Solving for x in Equation 1:**

- Divide both sides of Equation 1 by -45: x = -232 / -45 x = 5.16 (approximately)

**Solving for y in Equation 2:**

- Divide both sides of Equation 2 by 8: y = (12x + 12) / 8 y = (3x + 3) / 2

### Step 3: Substitute and Solve

**Substitute the value of x (5.16) into the equation for y:**

- y = (3 * 5.16 + 3) / 2
- y = (18.48) / 2
- y = 9.24 (approximately)

### Solution

Therefore, the solution to the system of linear equations is **x = 5.16 and y = 9.24**.

**Important Note:** This solution is an approximate solution, as we rounded the value of x during the process. You can use these approximate values to verify the solutions in the original equations.