To solve the system of equations given by:
- \( 2x + 3y = 12 \) (Equation 1)
- \( x + y = 5 \) (Equation 2)
We can use the substitution or elimination method. Here, I'll use the substitution method.
From Equation 2, we can express \( x \) in terms of \( y \):
\[ x = 5 - y \]
Now, we can substitute this expression for \( x \) into Equation 1:
\[ 2(5 - y) + 3y = 12 \]
Expanding this, we get:
\[ 10 - 2y + 3y = 12 \]
Combining like terms:
\[ 10 + y = 12 \]
Now, isolate \( y \):
\[ y = 12 - 10 \] \[ y = 2 \]
Now that we know \( y \), we can substitute back to find \( x \):
\[ x = 5 - y = 5 - 2 = 3 \]
Thus, the solution to the system of equations is:
\[ x = 3, \quad y = 2 \]
So, the final answer is:
\[ (x, y) = (3, 2) \]