To find the value of \( a \) in the expression \( 2.4x - 3.9y - 1.2x + ay \) that is equivalent to \( 1.2x + 1.2y \), we can start by simplifying the left side of the equation.
First, we combine the like terms in the expression \( 2.4x - 1.2x \):
\[ 2.4x - 1.2x = (2.4 - 1.2)x = 1.2x \]
Now, we rewrite the left side:
\[ 1.2x - 3.9y + ay \]
Next, we want this expression to equal \( 1.2x + 1.2y \). Therefore, we set up the equation:
\[ 1.2x - 3.9y + ay = 1.2x + 1.2y \]
Since \( 1.2x \) appears on both sides, we can subtract \( 1.2x \) from both sides:
\[ -3.9y + ay = 1.2y \]
Now we can isolate the terms involving \( y \):
\[ ay - 3.9y = 1.2y \]
Factoring out \( y \) gives us:
\[ (a - 3.9)y = 1.2y \]
To find \( a \), we can set the coefficients equal since this must hold for all \( y \):
\[ a - 3.9 = 1.2 \]
Now, solving for \( a \):
\[ a = 1.2 + 3.9 \] \[ a = 5.1 \]
Thus, the value of \( a \) is:
\[ \boxed{5.1} \]
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