Alg3.1.8

Solve $23x-17y+11=0,31x+13y-57=0\,$

Given $23x-17y+11=0,31x+13y-57=0\,$

By using cross multiplication method,

$\frac{x}{(-17)(-57)-(13)(11)}=\frac{y}{11\cdot31+57\cdot23}=\frac{1}{23\cdot13+31\cdot17}\,$

$x=\frac{969-143}{299+527},y=\frac{341+1311}{299+527}\,$

$x=\frac{826}{826},y=\frac{1652}{826}\,$

$x=1,y=2\,$