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## Sagot :

### Given Points:

1. [tex]\((9, 6)\)[/tex]

2. [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex]

3. [tex]\((-5, 9)\)[/tex]

### Equation:

[tex]\[ |x-2| - y = 1 \][/tex]

#### Step-by-Step Analysis:

### (a) Point [tex]\((9, 6)\)[/tex]:

1. For [tex]\( x = 9 \)[/tex], compute [tex]\( |x-2| \)[/tex]:

[tex]\[ |9-2| = |7| = 7 \][/tex]

2. Subtract [tex]\( y \)[/tex] from the result:

[tex]\[ 7 - 6 = 1 \][/tex]

3. We found that [tex]\( |9-2| - 6 = 1 \)[/tex]. Hence, [tex]\((9, 6)\)[/tex] satisfies the equation. Therefore, [tex]\((9, 6)\)[/tex] is a solution.

### (b) Point [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex]:

1. For [tex]\( x = \frac{1}{7} \)[/tex], compute [tex]\( |x-2| \)[/tex]:

[tex]\[ \left| \frac{1}{7} - 2 \right| = \left| \frac{1}{7} - \frac{14}{7} \right| = \left| -\frac{13}{7} \right| = \frac{13}{7} \][/tex]

2. Subtract [tex]\( y \)[/tex] from the result:

[tex]\[ \frac{13}{7} - \frac{6}{7} = \frac{13-6}{7} = \frac{7}{7} = 1 \][/tex]

3. We found that [tex]\( \left| \frac{1}{7} - 2 \right| - \frac{6}{7} = 1 \)[/tex]. Hence, [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] satisfies the equation. Therefore, [tex]\((\frac{1}{7}, \frac{6}{7})\)[/tex] is a solution.

### (c) Point [tex]\((-5, 9)\)[/tex]:

1. For [tex]\( x = -5 \)[/tex], compute [tex]\( |x-2| \)[/tex]:

[tex]\[ |-5 - 2| = |-7| = 7 \][/tex]

2. Subtract [tex]\( y \)[/tex] from the result:

[tex]\[ 7 - 9 = -2 \][/tex]

3. We found that [tex]\( |-5-2| - 9 = -2 \)[/tex], which does not equal 1. Hence, [tex]\((-5, 9)\)[/tex] does not satisfy the equation. Therefore, [tex]\((-5, 9)\)[/tex] is not a solution.

### Summary:

- [tex]\((9, 6)\)[/tex] is a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].

- [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] is a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].

- [tex]\((-5, 9)\)[/tex] is not a solution to the equation [tex]\( |x-2| - y = 1 \)[/tex].

So the results are:

(a) [tex]\((9,6)\)[/tex] is a solution.

(b) [tex]\(\left(\frac{1}{7}, \frac{6}{7}\right)\)[/tex] is a solution.

(c) [tex]\((-5,9)\)[/tex] is not a solution.