To solve the system of equations, we use the elimination method:
Step 1: Write the equations
[ \begin{cases} 2x + 3y = 12 \quad \text{(Equation 1)} \ 3x - 4y = 1 \quad \text{(Equation 2)} \end{cases} ]
Step 2: Eliminate (y)
Multiply Equation 1 by 4 and Equation 2 by 3 to make the coefficients of (y) opposites:
[
\begin{cases}
8x + 12y = 48 \quad \text{(Equation 1 × 4)} \
9x - 12y = 3 \quad \text{(Equation 2 × 3)}
\end{cases}
]
Add the two equations:
[
8x + 9x + 12y - 12y = 48 + 3 \
17x = 51 \
x = 3
]
Step 3: Find (y)
Substitute (x=3) into Equation 1:
[
2(3) + 3y = 12 \
6 + 3y = 12 \
3y = 6 \
y = 2
]
Answer: (x=3), (y=2)
(\boxed{x=3, y=2})
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