How many solutions does the system formed by x - y = 9 and
ay - ax + 90 = 0 have for a nonzero number a ? Give your answer and
complete the explanation.
a
The system has (select) solution(s). Rearranging the left side of the
2nd equation and subtracting 9a from both sides gives -ax + ay =
Dividing both sides by -a gives x - y = So, the equations describe
the same line.

Step-by-step explanation:

If you read through the bottom paragraph, you see it concludes with, "the equations describe the same line." This means the system has infinite solutions, because the two lines intersect everywhere.

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The rest of the solution is described in the paragraph. Starting with the rearranged form

  -ax +ay +9a = 0

"subtract 9a from both sides" means you now have ...

  -ax +ay +9a -9a = 0 -9a

or

  -ax +ay = -9a . . . . . . . . "-9" goes in the first box

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Now, dividing by -a gives you ...

  (-ax)/(-a) +(ay)/(-a) + (-9a)/(-a)

  x - y = 9 . . . . . . . . . . . . "9" goes in the second box, confirmed by the following statement that the equations (this, and x - y = 9) "describe the same line".

1 - Y-axis reflection

2 - translation of 6 to the left

3 - x-axis reflection

4 - translation of 6 to the left and down 4

5 - translation of 3 to the left and down 6

Step-by-step explanation: