Solve y=30x-6: Finding y When x=2

Q: Do I need to use parentheses when substituting?

Yes! When substituting $ x = 2 $ into $ 30x $, write it as 30(2) to make the multiplication clear and avoid confusion.

Q: What if I get a different answer than the choices?

Double-check your order of operations! Make sure you multiply $ 30 \times 2 = 60 $ first, then subtract 6. The most common error is doing subtraction before multiplication.

Q: How do I know which operation to do first?

Follow PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). In $ 30(2) - 6 $, multiplication comes before subtraction.

Q: Can I check my answer somehow?

Absolutely! Substitute your answer back: if $ y = 54 $ and $ x = 2 $, then $ 54 = 30(2) - 6 = 60 - 6 = 54 $ ✓

Q: Why is this called a linear equation?

Linear equations have variables raised only to the first power (like $ x $, not $ x^2 $). They create straight lines when graphed, hence the name 'linear'.

Linear Substitution with Integer Values

Find a $y$ when x=2

$y=30x-6$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's find Y using the given X value.

00:10 First, substitute the X value into the equation.

00:24 Next, perform the multiplication carefully.

00:28 Then, subtract as instructed.

00:31 And that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find a $y$ when x=2

$y=30x-6$

Step-by-step solution

To solve this problem, we'll follow these steps:

Substitute the given value of $x$ into the equation $y = 30x - 6$ .
Perform the necessary arithmetic to solve for $y$ .

Now, let's work through these steps:
Step 1: The problem gives us $x = 2$ and the equation $y = 30x - 6$ .
Step 2: Substitute $x = 2$ into the equation:
$y = 30(2) - 6$

Step 3: Calculate the expression:
$\begin{aligned} y &= 30 \times 2 - 6 \\ y &= 60 - 6 \\ y &= 54 \end{aligned}$

The solution to the problem is $y = 54$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Substitution: Replace the variable with given numerical value
Order: Multiply first: $30(2) = 60$ , then subtract 6
Verify: Check $30(2) - 6 = 60 - 6 = 54$ ✓

Common Mistakes

Avoid these frequent errors

Incorrect order of operations when calculating
Don't subtract first: 30(2-6) = 30(-4) = -120! This ignores proper order of operations and gives a completely wrong answer. Always multiply 30(2) first, then subtract 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

Do I need to use parentheses when substituting?

Yes! When substituting $x = 2$ into $30x$ , write it as 30(2) to make the multiplication clear and avoid confusion.

What if I get a different answer than the choices?

Double-check your order of operations! Make sure you multiply $30 \times 2 = 60$ first, then subtract 6. The most common error is doing subtraction before multiplication.

How do I know which operation to do first?

Follow PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). In $30(2) - 6$ , multiplication comes before subtraction.

Can I check my answer somehow?

Absolutely! Substitute your answer back: if $y = 54$ and $x = 2$ , then $54 = 30(2) - 6 = 60 - 6 = 54$ ✓

Why is this called a linear equation?

Linear equations have variables raised only to the first power (like $x$ , not $x^2$ ). They create straight lines when graphed, hence the name 'linear'.

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