Solve y = 2 + 6x: Finding y When x Equals 2

Q: Why do I multiply 6 × 2 before adding 2?

Because of the order of operations (PEMDAS)! Multiplication comes before addition, so you must calculate $ 6 \times 2 = 12 $ first, then add 2 to get 14.

Q: What if I accidentally calculated 2 + 6 = 8 first?

That's a common mistake! If you add first, you get $ 8 \times 2 = 16 $, which is wrong. Remember: multiplication always comes before addition unless there are parentheses.

Q: How can I check if my answer y = 14 is correct?

Substitute back into the original equation: $ y = 2 + 6(2) $. Calculate step by step: $ 6 \times 2 = 12 $, then $ 2 + 12 = 14 $. Since this matches your answer, you're correct!

Q: What does it mean to 'find y when x = 2'?

It means you need to substitute the value x = 2 into the equation and calculate what y equals. Think of it as replacing x with 2 everywhere you see it in the equation.

Q: Can I solve this without showing all the steps?

While you might be able to do it in your head, always show your work! Writing out the substitution and calculation steps helps prevent errors and shows your teacher you understand the process.

Linear Equations with Direct Substitution

Find a y when x=2

$y=2+6x$

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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

00:04 Substitute the X value according to the given data

00:10 Calculate the multiplication

00:18 We'll sum up

00:21 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

$y=2+6x$

Step-by-step solution

To solve this problem, we'll substitute the given value of $x = 2$ into the equation $y = 2 + 6x$ .
1. Substitute $x = 2$ into the equation:
$\begin{aligned} y &= 2 + 6x \\ &= 2 + 6 \times 2 \end{aligned}$

2. Perform the multiplication $6 \times 2$ :
$6 \times 2 = 12$

3. Add the result to 2:
$\begin{aligned} y &= 2 + 12 \\ &= 14 \end{aligned}$

Thus, when $x = 2$ , the value of $y$ is $\mathbf{14}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace the variable with the given value directly
Order of Operations: Calculate $6 \times 2 = 12$ first, then add 2
Verification: Check that $y = 2 + 6(2) = 14$ is correct ✓

Common Mistakes

Avoid these frequent errors

Forgetting order of operations when substituting
Don't calculate 2 + 6 = 8 first, then multiply by 2 = 16! This ignores multiplication priority and gives wrong answers. Always multiply 6 × 2 = 12 first, then add 2 to get 14.

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 do I multiply 6 × 2 before adding 2?

Because of the order of operations (PEMDAS)! Multiplication comes before addition, so you must calculate $6 \times 2 = 12$ first, then add 2 to get 14.

What if I accidentally calculated 2 + 6 = 8 first?

That's a common mistake! If you add first, you get $8 \times 2 = 16$ , which is wrong. Remember: multiplication always comes before addition unless there are parentheses.

How can I check if my answer y = 14 is correct?

Substitute back into the original equation: $y = 2 + 6(2)$ . Calculate step by step: $6 \times 2 = 12$ , then $2 + 12 = 14$ . Since this matches your answer, you're correct!

What does it mean to 'find y when x = 2'?

It means you need to substitute the value x = 2 into the equation and calculate what y equals. Think of it as replacing x with 2 everywhere you see it in the equation.

Can I solve this without showing all the steps?

While you might be able to do it in your head, always show your work! Writing out the substitution and calculation steps helps prevent errors and shows your teacher you understand the process.

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