I have been trying to solve the following equation but have not been able to figure out the solution. My textbook says that $x=4$ and $y=\frac{-5}{2}$. On inspection, I noticed that $25 - 5x + 2y \geqslant 0$ and also figured out that $y=\frac{1}{64}(-48x\pm 3\sqrt{1673-416x}+41)$ and hence $1673-416x \geqslant 0$. However, I feel like these inequalities are getting me nowhere since it still feels like there are infinite solutions. I was curious about how to continue (if I should continue at all); or is there a quicker approach to take which I have clearly ignored?
2026-04-09 00:01:22.1775692882
Solve the equation $2 \rvert 3x + 4y - 2 \lvert + 3\sqrt{25 - 5x + 2y} = 0$
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If the equation has a solution, then it must be if and only if
$$\begin{cases} 3x + 4y-2 =0 \\ 25 - 5x + 2y = 0\end{cases}$$
This is the simple linear system of equation.