RESOLVER SISTEMAS DE ECUACIONES MÉTODO DE SUSTITUCIÓN Super fácil - Para principiantes

How to Solve a 2x2 System of Equations Using Substitution

Introduction to Systems of Equations

• Daniel Carrión introduces the topic of solving a 2x2 system of equations using the substitution method.

• A 2x2 system consists of two equations with two unknowns, typically represented as x and y.

Steps in Solving the First Example

• The first equation is written down, replacing x with a parenthesis to prepare for substitution. The second equation states that x equals 5.

• By substituting x = 5 into the first equation (5 + y = 42), we combine like terms leading to 6y = 42.

• Dividing both sides by 6 gives y = 7, thus finding one variable's value.

Finding Values and Verification

• Substitute y back into the second equation (x = 5). This confirms that x equals 35 when calculated (5 * y).

• Both values are checked against the original equations:

• For x + y = 42: (35 + 7 = 42)

• For x = 5y: (35 = 5 * 7).

Second Example Setup

• Introduces another system: x + y = 41 and x - y = 5. The goal is again to find values for both variables.

• Rearranging the second equation gives us an expression for x in terms of y: x = y + 5.

Solving the Second Example

• Substituting this expression into the first equation leads to an operation where we simplify it down to find values for both variables.

• After calculations, it results in finding that y equals18 and subsequently calculating that x equals23.

Final Verification

• Both found values are substituted back into their respective original equations:

• For verification in the first equation: (23 +18 should equal41).

• In the second equation: confirming if (23 equals5 plus18).

Conclusion and Engagement

• Encourages viewers to try exercises on their own and share answers through comments or social media.