[tex]a) \\\left \{ {{y=\frac13x+3} \atop {y+x=7}} \right. \\\left \{ {{y=\frac13x+3} \atop {\frac13x+3+\frac33x=7}} \right. \\\left \{ {{y=\frac13x+3} \atop {\frac43x+3=7 /*3}} \right. \\\left \{ {{y=\frac13x+3} \atop {4x+9=21 /-9}} \right. \\\left \{ {{y=\frac13x+3} \atop {4x=12 /:4}} \right. \\\left \{ {{y=\frac13*3+3} \atop {x=3}} \right.\\\left \{ {{y=1+3} \atop {x=3}} \right.\\\left \{ {{y=4} \atop {x=3}} \right.\\A=(3, 4)[/tex]
b)
[tex]\left \{ {{y=-2x+2} \atop {4y+3x=-12}} \right. \\\left \{ {{y=-2x+2} \atop {4(-2x+2)+3x=-12}} \right. \\\left \{ {{y=-2x+2} \atop {-8x+8+3x=-12}} \right. \\\left \{ {{y=-2x+2} \atop {-5x+8=-12 /-8}} \right. \\\left \{ {{y=-2x+2} \atop {-5x=-20/:-5}} \right. \\\left \{ {{y=-2*4+2} \atop {x=4}} \right. \\\left \{ {{y=-8+2} \atop {x=4}} \right. \\\left \{ {{y=-6} \atop {x=4}} \right.[/tex]
[tex]B=(4, -6)[/tex]
c)
[tex]\left \{ {{3x-2y=4} \atop {3x-y=5 /*(-1)}} \right. \\\left \{ {{3x-2y=4} \atop {-3x+y=-5}} \right. \\-2y+y=4-5\\-y=-1\\y=1\\3x-1=5 /+1\\3x=6 /:3\\x=2\\C=(2, 1)[/tex]
d)
[tex]\left \{ {{y-2x=4} \atop {9x-2y=-3}} \right. \\\left \{ {{-2x+y=4/*9} \atop {9x-2y=-3/*2}} \right. \\\left \{ {{-18x+9y=36} \atop {18x-4y=-6}} \right. \\9y-4y=36-6\\5y=30/:5\\y=6\\6-2x=4 /-6\\-2x=4-6\\-2x=-2 /:(-2)\\x=1\\D=(1, 6)[/tex]
