Đáp án:a)\(\left \{ {{y=\frac{1}{2}} \atop {x=-1}} \right.\)
b)\(\left \{ {{y=0} \atop {x=\frac{-5}{3}}} \right.\)
c)\(\left \{ {{x=1} \atop {y=\frac{\sqrt{2}-1}{\sqrt{3}}}} \right.\)
Giải thích các bước giải:
a)\(\left \{ {{3(x-1)+2y=-x} \atop {5(x+y)=-3x+y-5}} \right.\)
⇔\(\left \{ {{3x+3+2y=-x} \atop {5x+5y=-3x+y-5}} \right.\)
⇔\(\left \{ {{4x+2y=-3} \atop {8x+6y=-5}} \right.\)
⇔\(\left \{ {{8x+4y=-6} \atop {8x+6y=-5}} \right.\)
⇔\(\left \{ {{-2y=-1} \atop {8x+6y=-5}} \right.\)
⇔\(\left \{ {{y=\frac{1}{2}} \atop {x=-1}} \right.\)
b)\(\left \{ {{2x+5=-(x+y)} \atop {6x+3y=y-10}} \right.\)
⇔\(\left \{ {{2x+5=-x-y} \atop {6x+3y=y-10}} \right.\)
⇔\(\left \{ {{3x+y=-5} \atop {6x-2y=-10}} \right.\)
⇔\(\left \{ {{6x+2y=-10} \atop {6x-2y=-10}} \right.\)
⇔\(\left \{ {{4y=0} \atop {6x-2y=-10}} \right.\)
⇔\(\left \{ {{y=0} \atop {x=\frac{-5}{3}}} \right.\)
c)\(\left \{ {{\sqrt{2}x-\sqrt{3}y=1} \atop {x+\sqrt{3}y=\sqrt{2}}} \right.\)
⇔\(\left \{ {{(\sqrt{2}+1)x=1+\sqrt{2}} \atop {x+\sqrt{3}y=\sqrt{2}}} \right.\)
⇔\(\left \{ {{x=1} \atop {y=\frac{\sqrt{2}-1}{\sqrt{3}}}} \right.\)
