Solve the following paris of linear (simultaneous) equation using method of elimination by substution:
1.5x + 0.1y = 6.2
3x - 0.4y = 11.2

Answer

To solve the given pair of linear equations using the method of elimination by substitution, we will follow these steps:

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

### Step 2: Solve one equation for one variable
Let's solve Equation 2 for \( x \):
\[ 3x = 11.2 + 0.4y \]
Now, divide both sides by 3:
\[ x = \frac{11.2 + 0.4y}{3} \]

### Step 3: Substitute the value of \( x \) into the other equation
Now, substitute the expression for \( x \) into Equation 1:
\[ 1.5\left(\frac{11.2 + 0.4y}{3}\right) + 0.1y = 6.2 \]

### Step 4: Simplify the equation
Multiply \( 1.5 \) with the fraction:
\[ \frac{1.5(11.2 + 0.4y)}{3} + 0.1y = 6.2 \]
This simplifies to:
\[ \frac{16.8 + 0.6y}{3} + 0.1y = 6.2 \]
Now, multiply through by 3 to eliminate the fraction:
\[ 16.8 + 0.6y + 0.3y = 18.6 \]

### Step 5: Combine like terms
Combine the \( y \) terms:
\[ 16.8 + 0.9y = 18.6 \]

### Step 6: Isolate \( y \)
Subtract \( 16.8 \) from both sides:
\[ 0.9y = 18.6 - 16.8 \]
\[ 0.9y = 1.8 \]
Now, divide by \( 0.9 \):
\[ y = \frac{1.8}{0.9} = 2 \]

### Step 7: Substitute back to find \( x \)
Now that we have \( y \), substitute \( y = 2 \) back into the expression for \( x \):
\[ x = \frac{11.2 + 0.4(2)}{3} \]
\[ x = \frac{11.2 + 0.8}{3} = \frac{12}{3} = 4 \]

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

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