Solving System Of Linear Equations: A Step-by-Step Guide for Success! Math Olympiad | A Very Nice Algebra Problem | X=? 👇 solving a system of linear equations |A-MATHS

Are you struggling to solve linear equations? Whether you're preparing for an exam or simply brushing up on your math skills, understanding how to solve linear equations is essential. In this post, we’ll focus on breaking down a specific system of linear equations: 2(x+10) = 70. You’ll discover how easy it is to find the solution by following a few simple steps. Let’s dive in and solve this equation together!

 

What is a Linear Equation?

A linear equation is one where the highest exponent of the variable is 1. These equations form straight lines when graphed and are among the simplest types of algebraic equations. They have a wide range of applications in real-world problems, from budgeting to physics.

The Equation: 2(x + 10) = 70

Let’s start by solving the given equation step by step:

2(x + 10) = 70

 

Step 1: Distribute the 2

To simplify the equation, distribute the 2 to both terms inside the parentheses:

2 * x + 2 * 10 = 70

This gives us:

2x + 20 = 70

 

Step 2: Isolate the Variable

 

Next, we want to isolate the variable x on one side of the equation. Start by subtracting 20 from both sides:

2x + 20 - 20 = 70 – 20

Simplifying both sides gives:

2x = 50

 

Step 3: Solve for x

Now, solve for x by dividing both sides by 2:

{2x}/{2} = {50}/{2}

This simplifies to:

x = 25

And there you have it! The solution to the equation 2(x + 10) = 70 is x = 25.

 

Step 4: Verifying the Solution

Always verify your solution by substituting x = 25 back into the original equation:

2(25 + 10) = 70

2(35) = 70

70 = 70

Since both sides of the equation are equal, the solution is correct.

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