Solve: `{:(3x - 2y = 4),(5x - 2y = 0):}`

Answer

To solve the system of equations:

1. **Equations Given:**
- \(3x - 2y = 4\) (Equation 1)
- \(5x - 2y = 0\) (Equation 2)

2. **Choose the Elimination Method:**
- Since both equations have the same coefficient for \(y\) (which is \(-2\)), we can eliminate \(y\) by subtracting one equation from the other.

3. **Subtract Equation 2 from Equation 1:**
\[ (3x - 2y) - (5x - 2y) = 4 - 0 \]
- This simplifies to:
\[ 3x - 5x - 2y + 2y = 4 \]
- Which further simplifies to:
\[ -2x = 4 \]

4. **Solve for \(x\):**
\[ x = \frac{4}{-2} = -2 \]

5. **Substitute \(x\) back into one of the original equations to find \(y\):**
- We can use Equation 2 for substitution:
\[ 5x - 2y = 0 \]
- Substitute \(x = -2\):
\[ 5(-2) - 2y = 0 \]
- This simplifies to:
\[ -10 - 2y = 0 \]
- Rearranging gives:
\[ -2y = 10 \]
- Solving for \(y\):
\[ y = \frac{10}{-2} = -5 \]

6. **Final Solution:**
- The solution to the system of equations is:
\[ x = -2, \quad y = -5 \]