Solve the pair of linear equations `2x+3y=11 and 2x-4y=-24`.

Answer

To solve the pair of linear equations \(2x + 3y = 11\) and \(2x - 4y = -24\), we can use the elimination method. Here’s a step-by-step solution:

### Step 1: Write down the equations
We have the following two equations:
1. \(2x + 3y = 11\) (Equation 1)
2. \(2x - 4y = -24\) (Equation 2)

### Step 2: Eliminate \(x\)
To eliminate \(x\), we can subtract Equation 1 from Equation 2. This will allow us to solve for \(y\).

\[ (2x - 4y) - (2x + 3y) = -24 - 11 \]

### Step 3: Simplify the equation
Now, simplify the left side:
\[ 2x - 4y - 2x - 3y = -24 - 11 \]
\[ -4y - 3y = -35 \]
\[ -7y = -35 \]

### Step 4: Solve for \(y\)
Now, divide both sides by -7:
\[ y = \frac{-35}{-7} = 5 \]

### Step 5: Substitute \(y\) back into one of the original equations
Now that we have \(y\), we can substitute it back into Equation 1 to find \(x\):
\[ 2x + 3(5) = 11 \]
\[ 2x + 15 = 11 \]

### Step 6: Solve for \(x\)
Subtract 15 from both sides:
\[ 2x = 11 - 15 \]
\[ 2x = -4 \]

Now, divide by 2:
\[ x = \frac{-4}{2} = -2 \]

### Final Solution
The solution to the pair of linear equations is:
\[ x = -2, \quad y = 5 \]