[tex]\displaystyle a). \left \{ {{x+y=-3} \atop {2x-y=4}} \right. \\ ~~~~~~------ \\ ~~~~~~~~3x~~/~~=1 \Rightarrow \boxed{x= \frac{1}{3} } \\ x+y=-3 \Rightarrow \frac{1}{3} +y=-3 \Rightarrow 1+3y=3 \cdot (-3) \Rightarrow 1+3y=-9 \Rightarrow \\ \Rightarrow 3y=-9-1 \Rightarrow 3y=-10 \Rightarrow \boxed{y=- \frac{10}{3} }[/tex]
[tex]\displaystyle b). \left \{ {{y=x+ \frac{1}{2} } \atop {x-4y=1}} \right. \Rightarrow \left \{ {{2y=2x+1} \atop {x-4y=1\Rightarrow x=1+4y}} \right. \\ 2y=2x+1 \Rightarrow 2y=2(1+4y)+1 \Rightarrow 2y=2+8y+1 \Rightarrow \\ \Rightarrow 2y-8y=2+1 \Rightarrow -6y=3 \Rightarrow y=- \frac{3}{6}\Rightarrow \boxed{y=- \frac{1}{2} } \\ x=1+4y \Rightarrow x=1+4 \cdot \left(- \frac{1}{2}\right) \Rightarrow x=1- \frac{4}{2} \Rightarrow x=1-2 \Rightarrow \\ \Rightarrow \boxed{x=-1}[/tex]
