Solve Linear Equation y=x-8: Finding y When x=2

Q: Why is my answer negative when both numbers in the problem are positive?

Great observation! Even though x = 2 is positive, we're subtracting 8 from 2. When you subtract a larger number from a smaller number, you always get a negative result. Think of it like owing money: if you have $2 but owe $8, you're $6 in debt!

Q: What if I get confused about which number to substitute?

Look for the phrase "when x = [number]" in the problem. That number is what you substitute for x. In this case, "when x = 2" tells you to replace every x with 2.

Linear Substitution with Negative Results

Find a y when x=2

$y=x-8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find Y according to the given X value

00:06 Substitute the X value according to the given data

00:13 Subtract

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find a y when x=2

$y=x-8$

Step-by-step solution

To solve the problem, we will follow these steps:

Step 1: Substitute the given value of $x$ into the equation $y = x - 8$ .
Step 2: Simplify the expression to find the corresponding value of $y$ .

Now, let's apply these steps:

Step 1: Given the equation $y = x - 8$ , we substitute $x = 2$ :
$\begin{aligned} y &= 2 - 8 \end{aligned}$

Step 2: Simplify the expression:
$\begin{aligned} y &= -6 \end{aligned}$

Thus, the value of $y$ when $x = 2$ is $-6$ .

Therefore, the solution to the problem is $y = -6$ .

Final Answer

$-6$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace variable with given value in equation
Technique: Substitute x = 2 into y = x - 8 gives y = 2 - 8
Check: Verify y = -6 by confirming -6 = 2 - 8 ✓

Common Mistakes

Avoid these frequent errors

Sign errors when subtracting larger from smaller numbers
Don't calculate 2 - 8 as positive 6! This ignores the order of operations and sign rules. When subtracting a larger number from a smaller one, the result is always negative. Always remember: 2 - 8 = -6, not +6.

Practice Quiz

Test your knowledge with interactive questions

Calculate y given that $$ x=2 $$ and $$ y=x $$ .

FAQ

Everything you need to know about this question

Why is my answer negative when both numbers in the problem are positive?

Great observation! Even though x = 2 is positive, we're subtracting 8 from 2. When you subtract a larger number from a smaller number, you always get a negative result. Think of it like owing money: if you have $2 but owe $8, you're $6 in debt!

How do I know I substituted correctly?

Follow this simple check: wherever you see the variable (x), replace it with the given number (2). So $y = x - 8$ becomes $y = 2 - 8$ . The equation structure stays the same, only the variable changes!

What if I get confused about which number to substitute?

Look for the phrase "when x = [number]" in the problem. That number is what you substitute for x. In this case, "when x = 2" tells you to replace every x with 2.

Can I check my answer another way?

Yes! Substitute your answer back: if y = -6, then does -6 = 2 - 8? Calculate the right side: 2 - 8 = -6. Since both sides equal -6, your answer is correct!

Why do some problems have negative answers?

Negative answers are completely normal in math! They represent real situations like temperatures below zero, depths below sea level, or money owed. Don't worry if your answer is negative - just make sure your calculations are correct.

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