Bài 3:
a: \(\dfrac{x}{43}=\dfrac{1}{y}\)
=>\(x\cdot y=43\)
=>\(x\cdot y=1\cdot43=43\cdot1=\left(-1\right)\cdot\left(-43\right)=\left(-43\right)\cdot\left(-1\right)\)
=>\(\left(x,y\right)\in\left\{\left(1;43\right);\left(43;1\right);\left(-1;-43\right);\left(-43;-1\right)\right\}\)
b: \(\dfrac{x}{43}=\dfrac{-1}{y-3}\)
=>\(x\left(y-3\right)=-43\)
=>\(x\left(y-3\right)=1\cdot\left(-43\right)=\left(-1\right)\cdot43=43\cdot\left(-1\right)=\left(-43\right)\cdot1\)
=>\(\left(x;y-3\right)\in\left\{\left(1;-43\right);\left(-1;43\right);\left(43;-1\right);\left(-43;1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(1;-40\right);\left(-1;46\right);\left(43;2\right);\left(-43;4\right)\right\}\)
c: \(\dfrac{x+2}{11}=\dfrac{-1}{y-1}\)
=>\(\left(x+2\right)\left(y-1\right)=-11\)
=>\(\left(x+2\right)\left(y-1\right)=1\cdot\left(-11\right)=\left(-1\right)\cdot11=11\cdot\left(-1\right)=\left(-11\right)\cdot1\)
=>\(\left(x+2;y-1\right)\in\left\{\left(1;-11\right);\left(-1;11\right);\left(11;-1\right);\left(-11;1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(-1;-10\right);\left(-3;12\right);\left(9;0\right);\left(-13;2\right)\right\}\)
d: \(\dfrac{x-5}{13}=\dfrac{1}{y-2}\)
=>\(\left(x-5\right)\left(y-2\right)=13\cdot1=13\)
=>\(\left(x-5\right)\left(y-2\right)=1\cdot13=13\cdot1=\left(-1\right)\cdot\left(-13\right)=\left(-13\right)\cdot\left(-1\right)\)
=>\(\left(x-5;y-2\right)\in\left\{\left(1;13\right);\left(13;1\right);\left(-1;-13\right);\left(-13;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(6;15\right);\left(18;3\right);\left(4;-11\right);\left(-8;1\right)\right\}\)
