Solve `{:(2x + y = 23),(4x - y = 19):}`

Answer

To solve the system of equations given by:

1. \( 2x + y = 23 \) (Equation 1)
2. \( 4x - y = 19 \) (Equation 2)

we can follow these steps:

### Step 1: Add the two equations
We will add Equation 1 and Equation 2 to eliminate \(y\).

\[ (2x + y) + (4x - y) = 23 + 19 \]

This simplifies to:

\[ 2x + 4x + y - y = 42 \]

So, we have:

\[ 6x = 42 \]

### Step 2: Solve for \(x\)
Now, we can solve for \(x\) by dividing both sides by 6:

\[ x = \frac{42}{6} = 7 \]

### Step 3: Substitute \(x\) back into one of the original equations
Now that we have \(x\), we will substitute \(x = 7\) back into Equation 1 to find \(y\):

\[ 2(7) + y = 23 \]

This simplifies to:

\[ 14 + y = 23 \]

### Step 4: Solve for \(y\)
Now, we can solve for \(y\):

\[ y = 23 - 14 = 9 \]

### Final Solution
Thus, the solution to the system of equations is:

\[ x = 7, \quad y = 9 \]