Đáp án + Giải thích các bước giải:

We convert the equations into their standard forms:

$y = -\dfrac{1}{2}x + 6 \Rightarrow -\dfrac{1}{2}x - y = -6 (1)$

$y = \dfrac{3}{2}x - 2 \Rightarrow \dfrac{3}{2}x - y = 2 (2)$

For the system of equations formed by the equations $(1)$ and $(2)$, we can easily see that both equations have the same coefficients for $y ($that is $-1)$, so we can use the elimination method.

Subtract $(1)$ from $(2)$ to get:

$\begin{align} \dfrac{3}{2}x - y + \dfrac{1}{2}x + y &= 2 + 6
\\ 2x &= 8 \\ x &= 4 \end{align}$

Substitute $x = 4$ back into $(2)$ to get:

$\begin{align} \dfrac{3}{2} \cdot 4 - y &= 2
\\ 6 - y &= 2 \\ y &= 4 \end{align}$

Therefore, the solution is $(x, y) = (4, 4)$.