Đáp án:

`|x+3|+|x-y|=0`

Vì `|x+3|>=0,|x-y|>=0`

`=>|x-3|+|x-y|=0`

Dấu "=" xảy ra khi \(\begin{cases}x=3\\y=x=3\\\end{cases}\)

`|x-1|+(y-2)^2=0`

Vì `|x-1|>=0,(y-2)^2>=0`

`=>|x-1|+(y-2)^2>=0`

Dấu "=" xảy ra khi \(\begin{cases}x=1\\y=2\\\end{cases}\)

`|x-3|+|x-2y+1|=0`

Vì `|x-3|>=0,|x-2y+1|>=0`

`=>|x-3|+|x-2y+1|>=0`

Dấu "=" xảy ra khi \(\begin{cases}x=3\\y=\dfrac{x+1}{2}=2\\\end{cases}\)

`|x-2|+|3xy-5|=0`

Vì `|x-2|>=0,|3xy-5|>=0`

`=>|x-2|+|3xy-5|=0`

Dấu "=" xảy ra khi \(\begin{cases}x=2\\y=\dfrac56\\\end{cases}\)

`|x-2|-3|2-x|=-10`

`<=>-|x-2|-3|x-2|=-10`

`<=>-2|x-2|=-10`

`<=>|x-2|=5`

`<=>` \(\left[ \begin{array}{l}x-2=5\\x-2=-5\end{array} \right.\) 

`<=>` \(\left[ \begin{array}{l}x=7\\x=-3\end{array} \right.\) 

`|x-3|+|x-y+1|=0`

Vì `|x-3|>=0`

`|x-y+1|>=0`

`=>|x-3|+|x-y+1|=0`

Dấu "=" xảy ra khi \(\begin{cases}x=3\\y=x+1=4\\\end{cases}\)

`|x-1|+(y+5)^2020=0`

Vì `|x-1|>=0`

`(y+5)^2020>=0`

`=>|x-1|+(y+5)^2020>=0`

Dấu "=" xảy ra khi \(\begin{cases}x=1\\y=-5\\\end{cases}\)

a) `|x+3| + |x-y| =0`

Do `|x+3| ≥ 0; |x-y| ≥ 0`

`=> |x+3| + |x-y| ≥ 0`

Dấu "=" có khi:

`|x+3| = 0; |x-y| = 0`

`=> x+3 = 0; |x-y| = 0`

`=> x = -3; x-y = 0`

`=> x = -3; -3 -y = 0`

`=> x = -3; y = -3`

Vậy `x = -3; y = -3`

b) `|x-1| + (y-2)^2 =0`

Do `|x-1| ≥ 0; (y-2)^2 ≥ 0`

`=> |x-1| + (y-2)^2 ≥ 0`

Dấu "=" có khi:

`|x-1| = 0; (y-2)^2 = 0`

`=> x - 1 = 0; y - 2 = 0`

`=> x = 1; y = 2`

Vậy `x = 1; y = 2`

c) `|x-3| + |x-2y+1| =0`

Do `|x-3| ≥ 0; |x-2y+1| ≥ 0`

`=> |x-3| + |x-2y+1| ≥ 0`

Dấu "=" có khi:

`|x-3| =0; |x-2y+1| =0`

`=> x-3 =0; |x-2y+1| =0`

`=> x = 3; 3-2y+1 = 0`

`=> x = 3; 2 - 2y = 0`

`=> x = 3; 2y = 2`

`=> x = 3; y = 1`

Vậy `x = 3; y = 1`

d) `|x-2| + |3x .y-5| =0`

Do `|x-2| ≥ 0; |3x .y-5| ≥ 0`

`=> |x-2| + |3x .y-5| ≥ 0`

Dấu "=" có khi:

`|x-2| = 0; |3x .y-5| = 0`

`=> x-2 = 0; |3x .y-5| = 0`

`=> x = 2; 3 . 2 .y-5 = 0`

`=> x = 2; 6y-5 = 0`

`=> x = 2; 6y = 5`

`=> x = 2; y = 5/6`

Vậy `x = 2; y = 5/6`

e) `|x-2| - 3|2-x| =-10`

`=> 1|x-2| - 3|2-x| =-10`

Ta có: `|x-2| = |2-x|`

`=> (1-3)|x-2| = -10`

`=> -2|x-2| = -10`

`=> |x-2| = 5`

Th1: `x-2 = 5`

`=> x = 7`

Th1: `x-2 = -5`

`=> x = -3`

Vậy `x = -3` hoặc `7`

g) `|x-3|+ |x-y+1|=0`

Do `|x-3| ≥ 0;  |x-y+1| ≥ 0`

`=> |x-3|+ |x-y+1| ≥ 0`

Dấu "=" có khi:

`|x-3| ≥ 0;  |x-y+1| ≥ 0`

`=> x-3 = 0;  x-y+1 = 0`

`=> x = 3; 3-y+1 = 0`

`=> x = 3; 4-y = 0`

`=> x = 3; y=4`

Vậy `x = 3; y=4`

h) `|x-1| + (y+5)^2020 =0`

Do `|x-1| ≥ 0; (y+5)^2020 ≥ 0`

`=> |x-1| + (y+5)^2020 ≥ 0`

Dấu "=" có khi:

`|x-1| = 0; (y+5)^2020 = 0`

`=> x - 1 = 0; y + 5 = 0`

`=> x = 1; y = -5`

Vậy `x = 1; y = -5`

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