You've learned a super useful skill today: how to use substitution to figure out the correct value for a variable in an equation! By plugging in the given options and checking if the equation balances, you can confidently find the solution, just like we did for 'y' in 6*y - 18 = 42.

The Power of Proof by Substitution

Substitution allows you to test potential solutions and verify if they make an equation true. It's like being a detective, using the clues (the options) to find the right answer that satisfies the given conditions (the equation).

Understanding Substitution

Substitution – Replacing a variable in an equation with a specific numerical value. This is done to test if that value makes the equation true.
Checking for True Equations – The goal is to find a value for the variable that makes the left side of the equation equal to the right side.

Solving the Example Equation: 6*y - 18 = 42

The Equation – You are given the equation 6y - 18 = 42 and asked to find the value of y from a set of options. Remember that 6y means 6 imes y.
Testing Option A (y=0)
- Substitute 0 for y: 6 imes 0 - 18
- Calculate: 0 - 18 = -18
- Compare: -18 ≠ 42. So, y=0 is incorrect.
Testing Option B (y=4)
- Substitute 4 for y: 6 imes 4 - 18
- Calculate: 24 - 18 = 6
- Compare: 6 ≠ 42. So, y=4 is incorrect.
Testing Option C (y=10)
- Substitute 10 for y: 6 imes 10 - 18
- Calculate: 60 - 18 = 42
- Compare: 42 = 42. This is true! So, y=10 is the correct value.
Testing Option D (y=12)
- You can estimate this: 6 imes 12 is 72.
- Calculate: 72 - 18 = 54
- Compare: 54 ≠ 42. So, y=12 is incorrect.

Key Takeaway

Elimination Strategy – When solving multiple-choice problems like this, you can eliminate incorrect answers as you test them. This makes finding the correct solution more efficient.
The Correct Solution – The value y = 10 is the only one that makes the equation 6y - 18 = 42 true.

Cracking the Code: Finding the Unknown 'y'!