In a competition, all chips of the same color are worth the same number of (fractional) points.

In a competition, all chips of the same color are worth the same number of (fractional) points. if 2 yellow chips and 20 black chips totals 1 point, and 20 yellow chips and 2 black totals 19 points, how many more points is a yellow chip worth?

It is important to answer the question that is asked.

The question is not, "How much are the chips worth?" but "How many more points is a yellow chip worth?"

We have 2 equations

20y + 2b = 19
2y + 20b = 1

Subtract 2nd from 1st

18y - 18b = 18

Rearrange

18y = 18 + 18b

Divide by 18

y = 1 + b

A yellow chip is worth one more than a black chip.

2y + 20b = 1
20y + 2b = 19

multiply the first equation by 10 ==>
20y + 200b = 10
20y + 2b = 19
-------------------- (subtract)
-198b = 9
b = -9/198 = -1/22

2y - 20/22 = 1
2y = 42/22
y = 21/22

so yellows are worth 21/22 point
and blacks are worth -1/22

check: 20y + 2b = 20(21/22) - 2/22 = 21(10/11) - 1/11 = 209/11 = 19 checks

2y+20b=1
20y+2b=19

solve for y