联立求解给定的方程组。 $2x - 3y = 13,$ $3x - 12y = 42.$ 答案 x = ... y = ...

1. Make the coefficients of $y$ equal in both equations.

Given
$2x-3y=13 \quad \text{(1)}$
$3x-12y=42 \quad \text{(2)}$
Multiply (1) by $4$:
$8x-12y=52 \quad \text{(3)}$

2. Eliminate $y$ and solve for $x$.

Subtract (2) from (3):
$(8x-12y)-(3x-12y)=52-42$
$5x=10$
$x=2$

3. Substitute $x=2$ into one original equation to find $y$.

Substitute $x=2$ into (1):
$2(2)-3y=13$
$4-3y=13$
$-3y=9$
$y=-3$