Find the value of x and y
` x- y + 3 = 0, 2x + 3y - 4 = 0 `.

Answer

To solve the system of equations given by:

1. \( x - y + 3 = 0 \)
2. \( 2x + 3y - 4 = 0 \)

we will follow these steps:

### Step 1: Rewrite the equations in standard form
From the first equation, we can rearrange it to isolate \( y \):

\[ x - y + 3 = 0 \implies x - y = -3 \implies y = x + 3 \]

Now, we have:
1. \( y = x + 3 \) (Equation 1)
2. \( 2x + 3y - 4 = 0 \) (Equation 2)

### Step 2: Substitute \( y \) in Equation 2
Now, we will substitute \( y \) from Equation 1 into Equation 2:

\[ 2x + 3(x + 3) - 4 = 0 \]

### Step 3: Simplify the equation
Now, simplify the equation:

\[ 2x + 3x + 9 - 4 = 0 \]
\[ 5x + 5 = 0 \]

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

\[ 5x = -5 \implies x = -1 \]

### Step 5: Substitute \( x \) back to find \( y \)
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):

\[ y = x + 3 = -1 + 3 = 2 \]

### Final Solution
Thus, the values of \( x \) and \( y \) are:

\[ x = -1, \quad y = 2 \]