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4 votes
19/22
How many solutions?
3x+8 = 9+ 3x
Infinitely many solutions

1 Answer

1 vote

Answer: No solutions

Reason:

Subtract 3x from both sides. They cancel out and go away. The x term is fully eliminated and we're left with the equation 8 = 9, which is a false statement. Therefore, the original equation is always false regardless of what you pick for x. This is why there aren't any solutions.

Visually you can graph y = 3x+8 and y = 3x+9. You'll get parallel lines that never intersect. We need the lines to intersect if we wanted a solution point. Parallel lines have the same slope, but different y intercepts.

Because the system has no solutions, we consider the system inconsistent.

User Altareos
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