Question Number 12265 by frank ntulah last updated on 17/Apr/17
$${Determinant}\:{method}\:{can}\:{be}\:{used}\:{to}\:{solve} \\ $$$${the}\:{system}\:{below}?,\:\mathrm{if}\:\mathrm{yes}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{determinant}\:\mathrm{method}\:\mathrm{and} \\ $$$$\:\mathrm{if}\:\mathrm{no}\:\mathrm{solve}\:\mathrm{by}\:\mathrm{another}\:\mathrm{method} \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$${x}+{y}−{z}=\mathrm{8} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{2}{z}=\mathrm{3} \\ $$$$\left({give}\:{clear}\:{reason}\:{for}\:{your}\:{answer}\right) \\ $$
Commented by mrW1 last updated on 17/Apr/17
$${let}\:{u}={x}−{z},\:{the}\:{equation}\:{system}\:{can}\:{be} \\ $$$${transformed}\:{into} \\ $$$${u}+{y}=\mathrm{8} \\ $$$$\mathrm{2}{u}+{y}=\mathrm{3} \\ $$$${which}\:{can}\:{be}\:{solved}\:{by}\:{determinant} \\ $$$${method}\:{or}\:{any}\:{other}\:{method}. \\ $$$${y}=\mathrm{13} \\ $$$${u}=−\mathrm{5} \\ $$$$\Rightarrow{x}={any}\:{real}\:{number} \\ $$$$\Rightarrow{y}=\mathrm{13} \\ $$$$\Rightarrow{z}={x}−{u}={x}+\mathrm{5} \\ $$
Commented by frank ntulah last updated on 17/Apr/17
$$\mathrm{thanks},\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir} \\ $$