a)
[tex]\left \{ {{2x+3y=-5} \atop {x-4y=3/*(-2)}} \right. \\+\left \{ {{2x+3y=-5} \atop {-2x+8y=-6}} \right. \\\\--------\\\\2x-2x+3y+8y=-5-6\\11y=-11\\y = -1\\x - 4*(-1) = 3\\x +4=3\\x = 3-4\\x = -1[/tex]
b)
[tex]\left \{ {{(x-1)^2+3y=x^2-2} \atop {3x-5y=4}} \right. \\\left \{ {{x^2-2x+1+3y=x^2-2} \atop {3x-5y=4}} \right. \\\left \{ {{-2x+3y=-3 /*3} \atop {3x-5y=4 /*2}} \right. \\+\left \{ {{-6x+9y=-9} \atop {6x-10y=8}} \right. \\--------\\-6x+6x+9y-10y=-9+8\\-y=-1\\y=1\\3x-5*1=4\\3x-5=4\\3x=4+5\\3x=9\\x=3[/tex]
2.
a)
[tex]\left \{ {{2x+y=2} \atop {3x-y=8}} \right. \\\left \{ {{y = 2-2x} \atop {3x-y=8}} \right. \\3x-(2-2x)=8\\3x-2+2x=9\\5x=9+2\\5x=11\\x = \frac{11}5 = 2\frac15\\2*\frac{11}5+y=2\\\frac{22}5+y=2\\y = 2-\frac{22}5\\y = \frac{10}{5} - \frac{22}5\\y = -\frac{12}{5} = -2\frac25[/tex]
