Chapter 10 - Section 10.1 - Systems of Linear Equations in Two Variables - 10.1 Exercises - Page 689: 44

$(25, 1)$

Given system is- $u-30v$ = $-5$ __ eq.1 $-3u+80v$ = $5$ __ eq.2 Multiplying eq.1 by 3- $3u-90v$ = $-15$ __ eq.3 Adding eq.3 and eq.2 - $3u-90v-3u+80v$ = $-15+5$ i.e. $-10v$ = $-10$ i.e. $v$ = $1$ Substituting for $v$ in eq.1 $u-30(1)$ = $-5$ i.e. $u)$ = $-5+30$ i.e. $u)$ = $25$ Thus $(25, 1)$ is the solution of given system.