How to Solve Simple Linear Equations: The Case of x + y = 25 and x - y = 5

Mathematics introduces us daily to clever problems that sharpen our logic and problem-solving skills. One classic example involves two unknowns, represented by numbers x and y, and two straightforward equations:

  • x + y = 25
  • x - y = 5

Understanding the Context

These equations may seem simple, but mastering their solution sets a strong foundation for tackling more complex math challenges. Let’s walk through the step-by-step process of solving these equations using the elimination method — a powerful technique that leverages adding equations to eliminate variables and find answers quickly.

The Equations at a Glance

We start with:

Sean los números x e y. x + y = 25 y x - y = 5. Sumando estas ecuaciones: 2x = 30, por lo que x = 15.

Key Insights

  1. x + y = 25
  2. x - y = 5

Our goal is to find the values of x and y using these two simultaneous equations.

Step 1: Sum the Two Equations

The key strategy here is adding the equations. By aligning like terms vertically:

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Final Thoughts

  x + y = 25<br/>
+ x - y = 5  </p>
<hr/>
<p>2x      = 30<br/>

Notice how y and -y cancel each other out, simplifying the problem to:

2x = 30

Step 2: Solve for x

Divide both sides by 2 to isolate x:

x = 30 ÷ 2 = 15

Now that we know x equals 15, we can substitute this value into one of the original equations to find y.

Step 3: Solve for y