What is the solution to the system of equations $$ \left\{\begin{array}{l}2 x+3 y=1 \ 4 x-3 y=-25\end{array}\right. $$

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We start with the system of equations:
$$
\begin{cases}
2x + 3y = 1\[5mm]
4x - 3y = -25
\end{cases}
$$

**Step 1.** Add the two equations to eliminate $$y$$:
$$
(2x + 3y) + (4x - 3y) = 1 + (-25)
$$
Simplify the left-hand side and right-hand side:
$$
6x = -24
$$

**Step 2.** Solve for $$x$$:
$$
x = \frac{-24}{6} = -4
$$

**Step 3.** Substitute $$x = -4$$ back into one of the original equations. We use the first equation:
$$
2(-4) + 3y = 1
$$
Simplify:
$$
-8 + 3y = 1
$$

**Step 4.** Solve for $$y$$:
$$
3y = 1 + 8 = 9 \quad \Longrightarrow \quad y = \frac{9}{3} = 3
$$

The solution to the system is:
$$
\boxed{x = -4, \quad y = 3}
$$
The solution is $$ x = -4 $$ and $$ y = 3 $$.

What is the solution to the system of equations \[ \left\{\begin{array}{l}2 x+3 y=1 \\ 4 x-3 y=-25\end{array}\right. \]

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