If x =a , y = b is the solution of the pair of equation x - y = 2 and x + y = 4 then the value of 3a + 4b is …….. .

Answer

To solve the problem step by step, we start with the given equations and the information about the solution.

### Step 1: Write down the equations
We have two equations:
1. \( x - y = 2 \)
2. \( x + y = 4 \)

### Step 2: Substitute the values of x and y
Since we know that \( x = a \) and \( y = b \), we can substitute these into the equations:
1. \( a - b = 2 \) (from the first equation)
2. \( a + b = 4 \) (from the second equation)

### Step 3: Solve the equations
Now we have a system of equations:
1. \( a - b = 2 \)
2. \( a + b = 4 \)

We can add these two equations to eliminate \( b \):
\[ (a - b) + (a + b) = 2 + 4 \]
This simplifies to:
\[ 2a = 6 \]
Dividing both sides by 2 gives:
\[ a = 3 \]

### Step 4: Find the value of b
Now that we have \( a \), we can substitute it back into one of the equations to find \( b \). We'll use the second equation:
\[ a + b = 4 \]
Substituting \( a = 3 \):
\[ 3 + b = 4 \]
Subtracting 3 from both sides gives:
\[ b = 1 \]

### Step 5: Calculate \( 3a + 4b \)
Now that we have \( a = 3 \) and \( b = 1 \), we can find \( 3a + 4b \):
\[ 3a + 4b = 3(3) + 4(1) \]
Calculating this gives:
\[ = 9 + 4 = 13 \]

### Final Answer
Thus, the value of \( 3a + 4b \) is \( 13 \).

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