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30 votes
30 votes
Fill in the blanks so that the equation has infinitely many solutions.

5y + 6 + 7y = blank (6y + blank)

User Jscharf
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1 Answer

17 votes
17 votes

Answer:

5y +6 +7y = 2 (6y + 3 )

Explanation:

We can name the blanks 'a' and 'b'. Then we have ...

5y +6 +7y = a(6y +b)

This will have infinitely many solutions when both sides simplify to the same expression.

12y +6 = 6ay +ab

To have these expressions be the same, we must have ...

12 = 6a . . . . same coefficient of y

6 = ab . . . . same constant

The first of these equations tells us ...

a = 12/6 = 2

Then the second equation tells us ...

b = 6/a = 6/2 = 3

The equation with the blanks filled in is ...

5y +6 +7y = 2 (6y + 3 )

User Olivier Refalo
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3.1k points