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Question Number 73468 by mathocean1 last updated on 12/Nov/19

$$\mathrm{soit}\mathrm{le}\mathrm{systeme}\mathrm{suivant}$$$$\{\begin{array}{l}2\mathrm{s}+4\mathrm{c}+3\mathrm{t}=700\\ 3\mathrm{s}+2\mathrm{c}+2\mathrm{t}=500\end{array}$$$$8\mathrm{s}+7\mathrm{c}+8\mathrm{t}=...?...$$$$\mathrm{comment}\mathrm{determiner}\mathrm{le}\mathrm{resultat}...?...$$$$\mathrm{de}\mathrm{la}{3}^{\mathrm{e}}\mathrm{equation}?$$

Answered by MJS last updated on 13/Nov/19

$$\mathrm{we}\mathrm{have}3\mathrm{unknown}\mathrm{and}2\mathrm{equations}\Rightarrow$$$$\Rightarrow \mathrm{solution}\mathrm{is}\mathrm{parametric}$$$$2s+4c+3t=700\Rightarrow s=-2c-\frac{3}{2}t+350$$$$3s+2c+2t=500\Rightarrow s=-\frac{2}{3}c-\frac{2}{3}t+\frac{500}{3}$$$$-2c-\frac{3}{2}t+350=-\frac{2}{3}c-\frac{2}{3}t+\frac{500}{3}\Rightarrow$$$$\Rightarrow t=-\frac{8}{5}c+220$$$$\Rightarrow s=\frac{2}{5}c+20$$$$8s+7c+8t=-\frac{13}{5}c+1920$$$$\mathrm{we}\mathrm{can}\mathrm{choose}c\mathrm{and}\mathrm{get}\mathrm{all}\mathrm{the}\mathrm{other}\mathrm{values}$$

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