Solve using the method of elimination by equating coefficients :
`x + y = 3.3 and ( -0.6 )/(3x - 2y) = 1.

Answer

To solve the given simultaneous equations using the method of elimination by equating coefficients, we will follow these steps:

### Step 1: Write down the equations
We have the following two equations:
1. \( x + y = 3.3 \) (Equation 1)
2. \( \frac{-0.6}{3x - 2y} = 1 \) (Equation 2)

### Step 2: Rearrange Equation 2
To make Equation 2 easier to work with, we can rearrange it:
\[ -0.6 = 3x - 2y \]
This can be rewritten as:
\[ 3x - 2y = -0.6 \quad \text{(Equation 2)} \]

### Step 3: Multiply Equation 1 to match coefficients
To eliminate one variable, we can multiply Equation 1 by 3:
\[ 3(x + y) = 3(3.3) \]
This results in:
\[ 3x + 3y = 9.9 \quad \text{(Equation 3)} \]

### Step 4: Set up for elimination
Now we have:
1. \( 3x + 3y = 9.9 \) (Equation 3)
2. \( 3x - 2y = -0.6 \) (Equation 2)

### Step 5: Subtract Equation 2 from Equation 3
We will subtract Equation 2 from Equation 3:
\[ (3x + 3y) - (3x - 2y) = 9.9 - (-0.6) \]
This simplifies to:
\[ 3x + 3y - 3x + 2y = 9.9 + 0.6 \]
\[ 5y = 10.5 \]

### Step 6: Solve for \( y \)
Now, divide both sides by 5:
\[ y = \frac{10.5}{5} = 2.1 \]

### Step 7: Substitute \( y \) back to find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ x + 2.1 = 3.3 \]
Subtract \( 2.1 \) from both sides:
\[ x = 3.3 - 2.1 = 1.2 \]

### Final Answer
Thus, the solution to the simultaneous equations is:
\[ x = 1.2, \quad y = 2.1 \]

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