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