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The substitution method is a powerful tool in algebra that allows us to solve systems of equations by replacing one variable with its known value. It's like solving a puzzle by figuring out which piece fits where. In our exercise, we started with the equation:

• \(x + y = 5\)

We were given \(y = 3\). This means we can substitute 3 in place of \(y\) in the original equation. So our equation becomes:

• \(x + 3 = 5\)

Substituting makes equations easier to solve because it reduces the number of unknowns. Imagine the equation is a balancing scale. By substituting \(y\)'s value, all we need to do next is balance the scale to find \(x\).' It's a straightforward method, especially great for beginners to grasp and apply in more complex problems later on.

Basic algebra involves using operations like addition, subtraction, multiplication, and division to solve equations. Once we've substituted \(y\) with 3 in the equation \(x + 3 = 5\), our job is to isolate \(x\). This is done by removing the 3 that's added to \(x\).

• Subtract 3 from both sides: \(x + 3 - 3 = 5 - 3\)

The left side simplifies to \(x\) because the \(+ 3\) and \(- 3\) cancel each other out. The right side calculates to 2, so:

• \(x = 2\)

This step embodies the essence of basic algebra: manipulate equations to get the unknown by itself. Applying arithmetic operations symmetrically keeps the equation balanced, leading us to the solution.

Verifying solutions is a crucial final step to ensure that our answer is correct. It's like checking your work to boost confidence in the solution. After finding \(x = 2\), we substitute both \(x\) and \(y\) back into the original equation to verify:

• Original equation: \(x + y = 5\)

Substitute \(x = 2\) and \(y = 3\):

• \(2 + 3 = 5\)

Since both sides of the equation are equal, our solution is verified. Verifying ensures accuracy, and in algebra, it's a habit worth forming. This step reassures us that even if a mistake was made early on, it'd be caught during the problem-checking phase.