To solve the system of equations:

Step 1: Write the equations

Equation (1): (4x + 5y = 11)
Equation (2): (3x - 2y = 12)

Step 2: Eliminate (y)

Multiply Equation (1) by 2 and Equation (2) by 5 to make the coefficients of (y) opposites:

• Equation (1) ×2: (8x + 10y = 22) (Equation 3)
• Equation (2) ×5: (15x - 10y = 60) (Equation 4)

Step 3: Add Equations 3 and 4

(8x + 15x + 10y -10y = 22 +60)
(23x = 82)
(x = \frac{82}{23})

Step 4: Substitute (x = \frac{82}{23}) into Equation (2)

(3\left(\frac{82}{23}\right) -2y =12)
(\frac{246}{23} -2y =12)
(-2y =12 - \frac{246}{23} = \frac{276 -246}{23} = \frac{30}{23})
(y = -\frac{15}{23})

Answer: (x = \frac{82}{23}), (y = -\frac{15}{23})

(\boxed{x=\frac{82}{23}, y=-\frac{15}{23}}) (or in boxed form as per standard, but if separate boxes are needed: (\boxed{\frac{82}{23}}) and (\boxed{-\frac{15}{23}}))

But since the problem says "put your answer in the box", maybe combined: (\boxed{(\frac{82}{23}, -\frac{15}{23})})

Final Answer
(\boxed{(\dfrac{82}{23}, -\dfrac{15}{23})})

作者声明:本文包含人工智能生成内容。