Solve the Linear Equation: Finding y in 6+y=0

Q: Why do I subtract 6 instead of adding 6?

You need to undo what's being done to y. Since 6 is being added to y, you must subtract 6 to cancel it out. Think of it as the opposite operation!

Q: What does 'isolate the variable' mean?

Isolating means getting y by itself on one side of the equation. You want $ y = \text{something} $, not $ 6 + y = \text{something} $.

Q: Do I always subtract from both sides?

Yes! Whatever you do to one side of the equation, you must do to the other side too. This keeps the equation balanced, like a scale.

Linear Equations with Additive Inverse Operations

$6+y=0$

$y=\text{?}$

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Step-by-step video solution

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00:00 Solve

00:03 Let's isolate the unknown Y, and calculate

00:06 And this is the solution to the question

Step-by-step written solution

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Understand the problem

$6+y=0$

$y=\text{?}$

Step-by-step solution

To solve this linear equation, we need to isolate the variable $y$ . Here’s how:

We start with the equation:

$6 + y = 0$

To isolate $y$ , we subtract 6 from both sides of the equation. This is because we want $y$ by itself on one side of the equation:

$6 + y - 6 = 0 - 6$

On the left side, the $+6$ and $-6$ cancel each other out, leaving us with:

$y = -6$

Therefore, the solution to the equation $6 + y = 0$ is $y = -6$ .

Checking our solution against the provided choices, we see that the correct answer is choice 1: $y = -6$ .

Final Answer

$y=-6$

Key Points to Remember

Essential concepts to master this topic

Isolation Rule: Move constants to opposite side using inverse operations
Technique: Subtract 6 from both sides: 6 + y - 6 = 0 - 6
Check: Substitute back into original equation: 6 + (-6) = 0 ✓

Common Mistakes

Avoid these frequent errors

Adding 6 to both sides instead of subtracting
Don't add 6 to both sides when you see 6 + y = 12 + y, not y = -6! This moves the constant in the wrong direction. Always use the opposite operation - if you see +6, subtract 6 from both sides.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

Why do I subtract 6 instead of adding 6?

You need to undo what's being done to y. Since 6 is being added to y, you must subtract 6 to cancel it out. Think of it as the opposite operation!

What does 'isolate the variable' mean?

Isolating means getting y by itself on one side of the equation. You want $y = \text{something}$ , not $6 + y = \text{something}$ .

How do I know which operation to use?

Look at what's happening to your variable. If something is being added, subtract it. If something is being subtracted, add it. Use the opposite operation!

Why is the answer negative?

When you subtract 6 from 0, you get -6. This makes sense because $6 + (-6) = 0$ . Negative answers are perfectly normal in algebra!

Do I always subtract from both sides?

Yes! Whatever you do to one side of the equation, you must do to the other side too. This keeps the equation balanced, like a scale.

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