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Question Number 118640 by 281981 last updated on 18/Oct/20

Answered by MJS_new last updated on 19/Oct/20

$$1)$$$$x=-2\wedge y=0\mathrm{solves}\mathrm{all}\mathrm{given}\mathrm{equations}$$

Answered by 1549442205PVT last updated on 19/Oct/20

$$\{\begin{array}{l}2\mathrm{x}+3\mathrm{y}+4=0\left(1\right)\\ 3\mathrm{x}+4\mathrm{y}+6=0\left(2\right)\\ 4\mathrm{x}+5\mathrm{y}+8=0\left(3\right)\end{array}$$$$\mathrm{Substracting}\left(2\right)\mathrm{from}\left(3\right)\mathrm{we}\mathrm{get}$$$$\mathrm{x}+\mathrm{y}+2=0\left(4\right)\iff 2\mathrm{x}+2\mathrm{y}+4=0.\mathrm{Substract}$$$$\mathrm{this}\mathrm{equation}\mathrm{from}\left(1\right)\mathrm{we}\mathrm{get}\mathrm{y}=0,$$$$\mathrm{replace}\mathrm{into}\left(4\right)\mathrm{we}\mathrm{get}\mathrm{x}=-2$$$$\mathrm{Simce}\mathrm{the}\mathrm{equations}\left(1\right)\left(2\right)\left(3\right)\mathrm{obtained}$$$$\mathrm{from}\left(4\right)\mathrm{by}\mathrm{multiplying}\mathrm{two}\mathrm{sides}\mathrm{by}$$$$2,3,4\mathrm{respectively},\mathrm{so}(\mathrm{x},\mathrm{y})=(-2,0)\mathrm{is}$$$$\mathrm{unique}\mathrm{root}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{system}.\mathrm{Hence}$$$$\mathbf{we}\mathbf{choose}\mathbf{assert}1)$$

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