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

In this article, we will learn how to solve a system of linear equations using the substitution method. We will use the following example to illustrate the process:

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

**Step 1: Simplify the Equations**

First, let's simplify both equations by expanding the parentheses and combining like terms:

**Equation 1:** 7y + 21 - 2x - 4 = 14
**Equation 2:** 4y - 8 + 3x - 9 = 2

Now, let's rearrange the equations to get all the terms on one side of the equation:

**Equation 1:** 7y - 2x = -7
**Equation 2:** 4y + 3x = 15

**Step 2: Choose an Equation to Solve for One Variable**

Let's choose Equation 1 and solve for y:

**y = (2x + 7) / 7**

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

Now, substitute the expression for y into Equation 2:

**4((2x + 7) / 7) + 3x = 15**

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

Simplify the equation by multiplying both sides by 7 to eliminate the fraction:

**8x + 28 + 21x = 105**

Combine like terms:

**29x = 77**

Divide both sides by 29:

**x = 77 / 29**
**x = 2.69**

**Step 5: Substitute the Value of x back into One of the Original Equations**

Now that we have the value of x, substitute it back into Equation 1 to find the value of y:

**y = (2(2.69) + 7) / 7**
**y = (5.38 + 7) / 7**
**y = 12.38 / 7**
**y = 1.77**

**Step 6: Write the Solution**

The solution to the system of linear equations is:

**x = 2.69**
**y = 1.77**

Therefore, the values of x and y that satisfy both equations are x = 2.69 and y = 1.77.