Understanding How to Solve for y in Linear Equations

When it comes to algebra, it’s all about finding the value of the unknown. One of the fundamental skills every student tackles is solving linear equations. Take the equation (2y - 6 = 10) for instance. Sounds straightforward, right? Let’s break it down so that by the end of this journey, you’ll feel like a pro at isolating that elusive variable (y).

Starting Point: The Equation

We begin with a classic equation: (2y - 6 = 10). The goal here is crystal clear—our mission is to uncover the value of (y). But where do we start? You know what? It’s simpler than it seems.

Step One: Clear the Clutter

First things first, we need to get rid of that pesky -6 on the left side. Think of your equation like your room—if it's messy, you can’t find anything! To tidy it up, add 6 to both sides. Here’s how it looks:

[ 2y - 6 + 6 = 10 + 6 ]

This beautiful simplification takes us to:

[ 2y = 16 ]

Did you get that? You just cleaned up a bit of clutter. Nice work! Now let’s keep moving.

Step Two: Dividing to Shine

Next, we need to isolate (y). Similar to how you’d divide a pizza into slices to share with friends, you’ll divide both sides of the equation by 2. It’s like sharing the workload:

[ \frac{2y}{2} = \frac{16}{2} ]

And now we’ve arrived at:

[ y = 8 ]

Verify Your Answer — Tick-Tock, Time for a Check!

Let’s check our work. This is a crucial step many students neglect. After all, wouldn’t you want to confirm that the pizza you just divided is still delicious and evenly sliced? Let’s substitute our (y) value back into the original equation:

[ 2(8) - 6 = 10 ]

When you do the math, you get:

[ 16 - 6 = 10 ]

And guess what? It checks out! So, not only have we found that (y = 8) but we’ve also confirmed that it’s the right answer.

The Bigger Picture

Now that you have the shorthand for solving such equations, why stop there? Understanding these concepts is crucial, especially as you prepare for the Ontario Mathematics Proficiency Test. Having a solid grasp on equations like this is essential for tackling various problems that might pop up in your exams.

Final Thoughts

In the intricate world of mathematics, solving equations is much like unlocking doors to new possibilities. Each equation can lead you to greater understanding and mastery of mathematical concepts. Keep practicing these steps—who knows what you’ll discover next?

So, next time you see an equation staring you down, remember the steps: clear, divide, and verify. You’ve got this!