SISTEMA DE EQUAÇÕES DO 1º GRAU | MÉTODO DA ADIÇÃO

Introduction

This tutorial will guide you through solving first-degree systems of equations using the addition method, also known as the elimination method. This technique simplifies the process of finding the values of variables in a system, making it a valuable tool in algebra.

Step 1: Understand the System of Equations

Before applying the addition method, you need to identify the system of equations you are working with.

• A system of equations consists of two or more equations with the same variables.

For example

• Equation 1: 2x + 3y = 6
• Equation 2: 4x - y = 5

Step 2: Align the Equations

To prepare for the addition method, write the equations in a standard format.

• Ensure both equations are aligned vertically, making it easier to add or subtract them.
• For example:

  2x + 3y = 6
  4x -  y = 5
  

Step 3: Adjust the Coefficients

Next, you may need to manipulate the equations so that adding or subtracting them will eliminate one variable.

• To eliminate y, you can multiply the equations by necessary coefficients so the coefficients of y are opposites.

For instance

• Multiply Equation 1 by 1 (no change): 2x + 3y = 6
• Multiply Equation 2 by 3: 12x - 3y = 15

Step 4: Add the Equations

Now, add the two equations together.

• Adding the equations can eliminate one variable:

  (2x + 3y) + (12x - 3y) = 6 + 15
  

• This simplifies to:

  14x = 21
  

Step 5: Solve for the Variable

After eliminating one variable, solve for the remaining variable.

• Divide both sides by the coefficient:

  x = 21 / 14
  x = 3/2 or 1.5
  

Step 6: Substitute Back to Find the Other Variable

With the value of x known, substitute it back into one of the original equations to find y.

• Using Equation 1:

  2(3/2) + 3y = 6
  

• Simplify and solve for y:

  3 + 3y = 6
  3y = 3
  y = 1
  

Step 7: State the Solution

Finally, present the solution as a coordinate pair.

• The solution to the system is:

  (x, y) = (1.5, 1)
  

Conclusion

In this tutorial, you learned how to solve first-degree systems of equations using the addition method. Remember to align your equations, adjust coefficients to eliminate variables, and substitute back to find the solution. Practice this method with different systems to enhance your understanding and proficiency.