Solving `1.5x+0.1y=6.2 ` and `3x-0.4y=11.2` by substitution method.

Answer

To solve the equations \(1.5x + 0.1y = 6.2\) and \(3x - 0.4y = 11.2\) using the substitution method, follow these steps:

### Step 1: Write down the equations
We have the following equations:
1. \(1.5x + 0.1y = 6.2\) (Equation 1)
2. \(3x - 0.4y = 11.2\) (Equation 2)

### Step 2: Solve Equation 1 for \(x\)
From Equation 1, we can isolate \(x\):
\[ 1.5x = 6.2 - 0.1y \]
Now, divide both sides by \(1.5\):
\[ x = \frac{6.2 - 0.1y}{1.5} \]
Let’s name this as Equation 3.

### Step 3: Substitute Equation 3 into Equation 2
Now, substitute the expression for \(x\) from Equation 3 into Equation 2:
\[ 3\left(\frac{6.2 - 0.1y}{1.5}\right) - 0.4y = 11.2 \]
Multiply through by \(1.5\) to eliminate the fraction:
\[ 3(6.2 - 0.1y) - 0.4y \cdot 1.5 = 11.2 \cdot 1.5 \]
This simplifies to:
\[ 18.6 - 0.3y - 0.6y = 16.8 \]
Combine like terms:
\[ 18.6 - 0.9y = 16.8 \]

### Step 4: Solve for \(y\)
Now, isolate \(y\):
\[ -0.9y = 16.8 - 18.6 \]
\[ -0.9y = -1.8 \]
Divide by \(-0.9\):
\[ y = \frac{-1.8}{-0.9} = 2 \]

### Step 5: Substitute \(y\) back into Equation 3 to find \(x\)
Now that we have \(y\), substitute \(y = 2\) back into Equation 3:
\[ x = \frac{6.2 - 0.1(2)}{1.5} \]
\[ x = \frac{6.2 - 0.2}{1.5} = \frac{6.0}{1.5} = 4 \]

### Final Solution
Thus, the solution to the system of equations is:
\[ x = 4, \quad y = 2 \]