Solve : `5x-9y=3 and 5x-10y=-5`

Answer

To solve the system of equations \(5x - 9y = 3\) and \(5x - 10y = -5\), we can follow these steps:

### Step 1: Write down the equations
We have the following two equations:
1. \(5x - 9y = 3\) (Equation 1)
2. \(5x - 10y = -5\) (Equation 2)

### Step 2: Subtract Equation 2 from Equation 1
To eliminate \(5x\), we can subtract Equation 2 from Equation 1:
\[ (5x - 9y) - (5x - 10y) = 3 - (-5) \]
This simplifies to:
\[ -9y + 10y = 3 + 5 \]
\[ y = 8 \]

### Step 3: Substitute \(y\) back into one of the original equations
Now that we have \(y = 8\), we can substitute this value back into Equation 1 to find \(x\):
\[ 5x - 9(8) = 3 \]
This simplifies to:
\[ 5x - 72 = 3 \]
Adding 72 to both sides gives:
\[ 5x = 3 + 72 \]
\[ 5x = 75 \]

### Step 4: Solve for \(x\)
Now, divide both sides by 5:
\[ x = \frac{75}{5} = 15 \]

### Final Solution
The solution to the system of equations is:
\[ x = 15, \quad y = 8 \]