Question Number 10184 by ketto last updated on 29/Jan/17
$${if}\:\underset{−} {{a}}\:=\mathrm{2}{i}+\mathrm{3}{j}\:.\:\underset{−} {{b}}=\mathrm{19}−\mathrm{15}{j}\:{and}\: \\ $$$$\underset{−} {{c}}\:=\mathrm{5}{i}−\mathrm{7}{j}.\:{find}\:{the}\:{value}\:{of}\:{x}\:{such} \\ $$$${that}\:{x}\underset{−} {{a}}\:+\:{y}\underset{−} {{c}}\:={b} \\ $$$$ \\ $$
Answered by sandy_suhendra last updated on 29/Jan/17
$$\mathrm{x}\left(\mathrm{2i}+\mathrm{3j}\right)+\mathrm{y}\left(\mathrm{5i}−\mathrm{7j}\right)=\mathrm{19i}−\mathrm{15j} \\ $$$$\Rightarrow\mathrm{2x}+\mathrm{5y}=\mathrm{19}\:.....\left(×\mathrm{7}\right)\:\Rightarrow\mathrm{14x}+\mathrm{35y}=\mathrm{133} \\ $$$$\Rightarrow\mathrm{3x}−\mathrm{7y}=−\mathrm{15}\:..\left(×\mathrm{5}\right)\:\Rightarrow\mathrm{15x}−\mathrm{35y}=−\mathrm{75} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−−−−\left(+\right. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{29x}\:=\:\mathrm{58}\:\Rightarrow\:\mathrm{x}=\mathrm{2} \\ $$
Answered by chux last updated on 29/Jan/17
$$\:\:\:\:\:\mathrm{lets}\:\mathrm{try}\:\mathrm{these}..... \\ $$