**Solving Systems of Linear Equations using Substitution Method**

In this article, we will solve a system of linear equations using the substitution method. The system of equations is:

**Equation 1:** 7(y + 3) - 2x + 2 = 14
**Equation 2:** 4(y - 2) + 3(x - 3) = 2

**Step 1: Simplify the Equations**

Let's simplify both equations by combining like terms:

**Equation 1:** 7y + 21 - 2x + 2 = 14
=> 7y - 2x + 23 = 14
=> 7y - 2x = -9 ... (1)

**Equation 2:** 4y - 8 + 3x - 9 = 2
=> 4y + 3x - 17 = 2
=> 4y + 3x = 19 ... (2)

**Step 2: Solve One of the Equations for One Variable**

Let's solve Equation (1) for y:

7y - 2x = -9 => 7y = 2x - 9 => y = (2x - 9) / 7 ... (3)

**Step 3: Substitute the Expression into the Other Equation**

Now, substitute the expression for y from Equation (3) into Equation (2):

4((2x - 9) / 7) + 3x = 19

**Step 4: Simplify and Solve for x**

Simplify the equation by multiplying both sides by 7:

4(2x - 9) + 21x = 133 => 8x - 36 + 21x = 133 => 29x = 169 => x = 169 / 29 => x = 5.83 (approx.)

**Step 5: Substitute the Value of x into One of the Original Equations to Solve for y**

Now that we have the value of x, substitute it into Equation (3) to solve for y:

y = (2(5.83) - 9) / 7 => y = (11.66 - 9) / 7 => y = 2.66 / 7 => y = 0.38 (approx.)

**Solution**

The solution to the system of equations is x = 5.83 and y = 0.38.