To solve the system of equations:
Step 1: Write the equations
[ \begin{cases} 2x + 3y = 12 \quad \text{(Equation 1)} \ 3x + 2y = 13 \quad \text{(Equation 2)} \end{cases} ]
Step 2: Eliminate one variable
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of (x) equal:
- Equation 1 ×3: (6x + 9y = 36)
- Equation 2 ×2: (6x + 4y = 26)
Subtract the second new equation from the first:
[
(6x + 9y) - (6x + 4y) = 36 - 26 \
5y = 10 \
y = 2
]
Step 3: Find (x)
Substitute (y=2) into Equation 1:
[
2x + 3(2) = 12 \
2x + 6 = 12 \
2x = 6 \
x = 3
]
Answer: (x=3, y=2)
(\boxed{x=3, y=2}) (or in boxed form as per common practice, maybe (\boxed{3}) and (\boxed{2}), but since the question likely expects both, perhaps (\boxed{(3,2)}))
But if separate boxes are needed: (\boxed{3}) and (\boxed{2})
Assuming the problem expects the values, the final answer is (\boxed{3}) for x and (\boxed{2}) for y. However, if combined: (\boxed{(3,2)})
(\boxed{3})
(\boxed{2})
Or as a pair: (\boxed{(3,2)})
Given the usual format, probably (\boxed{3}) and (\boxed{2}), but let's confirm: the system solution is x=3, y=2, so the answer is (\boxed{3}) and (\boxed{2}). But if the problem wants a single box, maybe (\boxed{3 2}) but more likely separate. However, in many cases, the answer is written as (\boxed{(3,2)}).
Final answer: (\boxed{(3,2)})
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