Answer:
[tex]x=1\frac{83}{91}\\y=-2\frac{73}{91}[/tex]
Step-by-step explanation:
#Using the method of substitution and replacement of unknown values.
Given that
[tex]\frac{3}{2}x+\frac{2}{3}y=1...(i)\\and\\\frac{1}{6}x-\frac{3}{5}y=2...(ii)\\[/tex]
Express eqtn (ii) in terms of x
[tex]\frac{1}{6}x=2+\frac{3}{5}y\\x=12+\frac{18}{5}y[/tex]
Replacing for x in eqtn (i)
[tex]\frac{3}{2}(12+\frac{18}{5}y)+\frac{2}{3}y=1\\18+\frac{27}{5}y+\frac{2}{3}y=1\\18-1=-\frac{91}{15}y\\y=-2\frac{73}{91}[/tex]
Substitute y value in eqtn(ii) to obtain x
[tex]Y=-2\frac{73}{91}\\\frac{1}{6}x-\frac{3}{5}y=2\\x=2+\frac{3}{5}(-2\frac{73}{91})\\x=1\frac{83}{91}[/tex]
