$ 2 \mathrm{x}-5 \mathrm{y}=20 $
$ 3 \mathrm{x}+\mathrm{my}=\mathrm{m} $
$ \Rightarrow \mathrm{y}=\frac{2 \mathrm{~m}-60}{2 \mathrm{~m}+15} $
$ \mathrm{y}<0 \Rightarrow \mathrm{m} \in\left(\frac{-15}{2}, 30\right) $
$ \mathrm{x}=\frac{25 \mathrm{~m}}{2 \mathrm{~m}+15} $
$ \mathrm{x}<0 \Rightarrow \mathrm{m} \in\left(\frac{-15}{2}, 0\right) $
$ \Rightarrow \mathrm{m} \in\left(\frac{-15}{2}, 0\right) $
$ |\mathrm{A}|=2 \mathrm{~m}+15 $
$ \text { Now, } $
$ 8 \int_{-15}^0(2 \mathrm{~m}+15) \mathrm{dm}=8\left\{\mathrm{~m}^2+15 \mathrm{~m}\right\}_{\frac{-15}{2}}^0 $
$ \Rightarrow 8\left\{-\left(\frac{225}{4}-\frac{225}{2}\right)\right\} $
$ =8 \times \frac{225}{4}=450$
Now,
$ 8 \int_{\frac{-15}{2}}^0(2 \mathrm{~m}+15) \mathrm{dm}=8\left\{\mathrm{~m}^2+15 \mathrm{~m}\right\}_{\frac{-15}{2}}^0 $
$ \Rightarrow 8\left\{-\left(\frac{225}{4}-\frac{225}{2}\right)\right\} $
$ =8 \times \frac{225}{4}=450$
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