The equations defining a model of two trading nations are given by:

$Y_1=C_1+I_1^{*}+x_1-M_1$

$Y_2=C_2+I_2^{*}+x_2-M_2$

$C_1=0\mathrm{.}7Y_1+50$

$C_2=0\mathrm{.}80Y_2+100$

$I_1^{*}=200$

$I_2^{*}=300$

$M_1=0\mathrm{.}3Y_1$

$M_2=0\mathrm{.}1Y_2$

Let $Y$ be the total income in a country, $C$ aggregate consumption, $I^{*}$ be

autonomous investment, $x$ be the export, and $M$ be the import in a country.

Express the system in $2$ x $2$ matrix form and hence find the values of $Y_1$ and

$Y_2.$ Note that an export in one country is an import of the other country.