Объяснение:

1.

a)

[tex]\left \{ {{3x+y=1} \atop {2x-3y=-14}} \right. \ \ \ \ \ \left \{ {{y=1-3x} \atop {2x-3*(1-3x)=-14}} \right. \ \ \ \ \left \{ {{y=1-3x} \atop {2x-3+9x=-14}} \right. \ \ \ \ \left \{ {{y=1-3x} \atop {11x=-11\ |:11}} \right.\ \ \ \ \left \{ {{y=4} \atop {x=-1}} \right..[/tex]

Ответ: (-1;4).

b)

[tex]\left \{ {{2x-3*(y+1)=-2} \atop {3*(x+1)+3y=2y-1}} \right. \ \ \ \ \left \{ {{2x-3y-3=-2} \atop {3x+3+3y=2y-1}} \right. \ \ \ \ \left \{ {{2x-3y=1} \atop {y=-3x-4}} \right.\ \ \ \ \left \{ {{2x-3*(-3x-4)=1} \atop {y=-3x-4}} \right. \\\left \{ {{2x+9x+12=1} \atop {y=-3x-4}} \right. \ \ \ \ \left \{ {{11x=-11\ |:11} \atop {y=-3x-4}} \ \ \ \ \left \{ {{x=-1} \atop {y=-1}} \right. \right. .[/tex]

Ответ: (-1;-1).

c)

[tex]\left \{ {{2x-y=3} \atop {3x+2y=8}} \right.\ \ \ \ \left \{ {{y=2x-3} \atop {3x+2*(2x-3)=8}} \right.\ \ \ \ \left \{ {{y=2x-3} \atop {3x+4x-6=8}} \right. \ \ \ \ \left \{ {{y=2x-3} \atop {7x=14\ |:7}} \right. \ \ \ \ \left \{ {{y=1} \atop {x=2}} \right. .[/tex]

Ответ: (2;1).

d)

[tex]\left \{ {{3x-2*(3y+1)=-2} \atop {2*(x+1)-y=3x-1}} \right. \ \ \ \ \left \{ {{3x-6y-2=-2} \atop {2x+2-y=3x-1}} \right. \ \ \ \ \left \{ {{3x=6y\ |:3} \atop {y=3-x}} \right.\ \ \ \ \left \{ {{x=2y} \atop {y=3-x}} \right.\ \ \ \ \ \left \{ {{x=2*(3-x)} \atop {y=3-x}} \right. \\ \left \{ {{x=6-2x} \atop {y=3-x}} \right. \ \ \ \ \left \{ {{3x=6\ |:3} \atop {y=3-x}} \right. \ \ \ \ \left \{ {{x=2} \atop {y=1}} \right. .[/tex]

Ответ: (2;1).

2.

[tex]\left \{ {{4x-3y=5} \atop {5x=4y+6}} \right.\ \ \ \ \left \{ {{4x-3y=5\ |*4} \atop {5x-4y=6\ |*(-3)}} \right.\ \ \ \ \left \{ {{16x-12y=20} \atop {-15x+12y=-18}} \right. .[/tex]

Суммируем эти уравнения:

[tex]x=2.\ \ \ \ \Rightarrow\\-15*2+12y=-18\\-30+12y=-18\\12y=12\ |:12\\y=1.[/tex]

Ответ: (2;1).