Solve for y: y^2 - 9y = 0
Understand the Problem
The question requires us to solve for y in the given quadratic equation. We can factor out a y, then set each factor equal to zero and solve for y.
Answer
$y = 0, 9$
Answer for screen readers
$y = 0, 9$
Steps to Solve
- Factor out y
We factor the common term $y$ from the left side of the equation:
$y^2 - 9y = y(y - 9) = 0$
- Set each factor equal to zero
Now, for the product of two factors to be zero, at least one of them must be zero. Therefore we set each factor equal to zero:
$y = 0$ or $y - 9 = 0$
- Solve for y in each case
We already have one solution: $y = 0$. For the second equation, we add 9 to both sides:
$y - 9 + 9 = 0 + 9$ $y = 9$
Therefore, the two solutions are $y = 0$ and $y = 9$.
$y = 0, 9$
More Information
The equation $y^2 - 9y = 0$ is a quadratic equation. Quadratic equations can have up to two real solutions. In this case, we found two distinct real solutions for $y$.
Tips
A common mistake is to divide both sides of the equation by $y$. This would lead to the solution $y = 9$, but would miss the solution $y = 0$. Dividing by a variable can cause you to lose solutions if that variable could equal zero. Factoring is the preferred approach here.
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