MÉTODO DE IGUALACIÓN Super Facil

Understanding the Method of Equalization

Introduction to Key Concepts

• Daniel Carreón introduces the topic of equalization method, emphasizing its importance in solving equations.

• Defines an unknown variable (incógnita) as a value represented by letters x and y, and explains a system of equations as two or more equations sharing these variables.

Solving Equations Using the Equalization Method

• Presents the first example: x = 5y + 10 and x = 2y + 16, highlighting that both equations share the same variables.

• Explains how to set up the equalization by equating both expressions for x: 5y + 10 = 2y + 16.

Step-by-Step Solution Process

• Rearranges the equation to isolate y: 5y - 2y = 16 - 10.

• Simplifies to find y, resulting in 3y = 6, leading to y = 2.

Finding Value of X

• Substitutes y back into one of the original equations: x = 5(2) + 10.

• Calculates x, confirming that x = 20, validating results by substituting into both original equations.

Next Example with Different Equations

New System of Equations

• Introduces a new system: 3x - 4y = -6 and 2x + 4y = 16, noting they also share variables x and y.

Isolating X in Each Equation

• Rearranges first equation to express x:

[3x = -6 + 4y Rightarrow x = -6 + 4y/3].

• Does similarly for second equation:

[2x = 16 - 4y Rightarrow x = 16 - 4y/2].

Applying Equalization Method Again

• Sets both expressions for x equal:

[-6 + 4y/3 = 16 - 4y/2].

Solving for Y

• Cross-multiplies to eliminate fractions, leading to simplified terms on each side.

• Combines like terms after rearranging, ultimately finding that:

[20y =60 Rightarrow y =3.]

This structured approach provides clarity on how to apply the method of equalization effectively while solving systems of linear equations.

Finding the Value of X in an Equation

Solving for X

• The speaker begins by explaining how to find the value of X using one of two equations, choosing the second equation: 2x + 4y = 16.

• Substituting y = 3 into the equation results in 2x + 12 = 16. To isolate x, subtract 12 from both sides, leading to 2x = 4.

• Dividing both sides by 2 gives x = 2. Thus, the solution for this system of equations is x = 2 and y = 3.

Verification of Solutions

• The speaker verifies the solution by substituting values back into the first equation: 3x - 4y = -6. Replacing with known values yields 6 - 12 = -6, confirming correctness.

• The second equation is also checked: substituting into 2x + 4y = 16 gives 4 + 12 = 16, which holds true. Both equations are satisfied with these values.