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**Pair of Linear Equations in Two Variables - Revision Notes**

**Introduction:**
A pair of linear equations in two variables is a system of two equations that involve two variables and have the same solution. The general form of a pair of linear equations is:

ax + by = c
dx + ey = f

where a, b, c, d, e, and f are constants and x and y are the variables.

**Substitution Method:**

The substitution method is a technique used to solve a pair of linear equations by expressing one variable in terms of the other and substituting it into the other equation.

**Steps to solve a pair of linear equations using the substitution method:**

1. Choose one equation and express one variable in terms of the other variable.
2. Substitute the expression of the variable from step 1 into the other equation.
3. Solve the resulting equation to find the value of the remaining variable.
4. Substitute the value of the found variable back into any of the original equations to find the value of the other variable.
5. Verify the solution by substituting the values of x and y into both equations to check if they satisfy both equations.

**Example:**
Let's solve the following pair of linear equations using the substitution method:

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

Step 1: Choose Equation 2 and express y in terms of x:
4x - y = 1
=> y = 4x - 1

Step 2: Substitute the expression of y from Step 1 into Equation 1:
2x + 3(4x - 1) = 7

Step 3: Solve the resulting equation:
2x + 12x - 3 = 7
14x - 3 = 7
14x = 10
x = 10/14
x = 5/7

Step 4: Substitute the value of x back into Equation 2 to find y:
4(5/7) - y = 1
20/7 - y = 1
y = 20/7 - 1
y = 20/7 - 7/7
y = 13/7

Step 5: Verify the solution:
Substituting x = 5/7 and y = 13/7 into both equations:
Equation 1: 2(5/7) + 3(13/7) = 7
Equation 2: 4(5/7) - (13/7) = 1

Both equations are satisfied, so the solution to the pair of linear equations is x = 5/7 and y = 13/7.

**Conclusion:**
The substitution method is a useful technique for solving a pair of linear equations in two variables. By expressing one variable in terms of the other and substituting it into the other equation, we can find the values of both variables. Remember to verify the solution by substituting the values back into the original equations.