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4 votes
Solve each system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solution.

3x+6y=18
3y=-3/2x+9

1 Answer

3 votes
First, get one of the variables on its own. I'm going to do the first equation since it looks easier. :)


3x + 6y = 18
Subtract 6y from both sides.


3x = 18 - 6y
Divide both sides by 3 to get the variable alone.

x = 6 - 2y
Plug this into the other equation for x.


3y = - (3)/(2) (6 - 2y) + 9
Distribute.


3y = - 9 + 3y + 9
Add like terms.


3y = 3y
The system has infinitely many solutions because both sides equal each other.

Hope this helped!

:)
User Michael L
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