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

February 22, 2026

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

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:

x + y = 25
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:

  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

Use the first equation: x + y = 25 Substitute x = 15: 15 + y = 25

Subtract 15 from both sides: y = 25 – 15 = 10

Final Answer

The solutions to the equations are:

x = 15
y = 10

✅ Verification: Plug values back into the original equations:

x + y = 15 + 10 = 25 ✓
x - y = 15 – 10 = 5 ✓

Both verify correctly, confirming our solution.

Why This Method Works

By adding equations with opposite signs for y, the variable cancels out, reducing the problem to a single unknown (x). This method saves time and minimizes errors — especially useful in academic exams or real-world applications like budgeting and data analysis.

Bonus Tip: Solving with Elimination

When solving linear equations, try:

Adding equations to eliminate variables
Subtracting equations to eliminate variables
Altering one equation to match variable signs before adding
Finally substituting to find the remaining variables

In summary, using the elimination method to sum the equations x + y = 25 and x – y = 5 yields 2x = 30, giving x = 15 and y = 10 — a clear, efficient path to solving simple yet powerful equations.