a)
[tex]\left \{ {{x=2y+1} \atop {3x+y=10}} \right.[/tex] <=> [tex]\left \{ {{x = 2y+1} \atop {3*(2y+1) + y = 10}} \right.[/tex] <=> [tex]\left \{ {{x = 2y+1} \atop {6y+3+y = 10}} \right.[/tex] <=> [tex]\left \{ {{x = 2y+1} \atop {7y = 7}} \right.[/tex] <=> [tex]\left \{ {{x = 3} \atop {y = 1}} \right.[/tex]
b)
[tex]\left \{ {{x+4y = 3} \atop {x-4y = -7}} \right.[/tex] => 2x = 3-7 = -4 <=> x = -2 => [tex]\left \{ {{4y = 3-x} \atop {x = -2}} \right.[/tex] <=> [tex]\left \{ {{y = 5/4} \atop {x=2}} \right.[/tex]
c)
[tex]\left \{ {{2x-y = 3 | *2} \atop {3x+2y = 1}} \right.[/tex] <=> [tex]\left \{ {{4x-2y = 6} \atop {3x+2y = 1}} \right.[/tex] => 7x = 7 <=> x = 1 => [tex]\left \{ {{x=1} \atop {y = -1}} \right.[/tex]
d)
[tex]\left \{ {{0.2x -0.3y = 0.7 |*10} \atop {1.2x - 1.4y = 1 |*10}} \right.[/tex] <=>[tex]\left \{ {{2x -3y = 7} \atop {12x - 14y = 10}} \right.[/tex] <=> [tex]\left \{ {{2x = 7+3y} \atop {6*(7+3y) - 14y = 10}} \right.[/tex] <=> [tex]\left \{ {{2x = 7+3y} \atop {42+4y = 10}} \right.[/tex] <=> [tex]\left \{ {{2x = 7-24} \atop {y = -8}} \right.[/tex] <=> [tex]\left \{ {{x = -8.5} \atop {y = -8}} \right.[/tex]
