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Question Number 29259 by Abdul Gani last updated on 06/Feb/18
solve the equation  2x+3y=5  3x+4y=4
$${solve}\:{the}\:{equation} \\ $$$$\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{5} \\ $$$$\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{4}\: \\ $$
Answered by Joel578 last updated on 06/Feb/18
2x + 3y = 5 ... (i)  3x + 4y = 4 ... (ii)  Multiply equation (i) with 3 and equation (ii) with 2  ⇒ 6x + 9y = 15         6x + 8y = 8  Eliminate both equations  ⇒ y = 7  Substitute y = 7 into (i) or (ii) gives you x = −8
$$\mathrm{2}{x}\:+\:\mathrm{3}{y}\:=\:\mathrm{5}\:…\:\left({i}\right) \\ $$$$\mathrm{3}{x}\:+\:\mathrm{4}{y}\:=\:\mathrm{4}\:…\:\left({ii}\right) \\ $$$$\mathrm{Multiply}\:\mathrm{equation}\:\left({i}\right)\:\mathrm{with}\:\mathrm{3}\:\mathrm{and}\:\mathrm{equation}\:\left({ii}\right)\:\mathrm{with}\:\mathrm{2} \\ $$$$\Rightarrow\:\mathrm{6}{x}\:+\:\mathrm{9}{y}\:=\:\mathrm{15} \\ $$$$\:\:\:\:\:\:\:\mathrm{6}{x}\:+\:\mathrm{8}{y}\:=\:\mathrm{8} \\ $$$$\mathrm{Eliminate}\:\mathrm{both}\:\mathrm{equations} \\ $$$$\Rightarrow\:{y}\:=\:\mathrm{7} \\ $$$$\mathrm{Substitute}\:{y}\:=\:\mathrm{7}\:\mathrm{into}\:\left({i}\right)\:\mathrm{or}\:\left({ii}\right)\:\mathrm{gives}\:\mathrm{you}\:{x}\:=\:−\mathrm{8} \\ $$

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