Let's start by substituting the value of \( g = 12 \) into the second equation \( t = 21 - g \) to find the value of \( t \).
Substituting:
\[ t = 21 - 12 \]
Calculating:
\[ t = 9 \]
Now we have the values:
\[ g = 12 \quad \text{and} \quad t = 9 \]
To verify, we can plug these values back into the first equation \( 3t + 2g = 51 \):
\[ 3(9) + 2(12) = 27 + 24 = 51 \]
Since this is true, the solutions are:
\[ t = 9 \quad \text{and} \quad g = 12 \]
So, to answer your original question: No, I still needed to find the value of \( t \); the correct solutions are \( t = 9 \) and \( g = 12 \).
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