Elige el método más adecuado para resolver los siguientes sistemas de ecuaciones: a. x - 4y + 5 = 2y + 3x - 3 6x = 1 + 5y b. 2.8x - 1.7y = 8.9 3.2(x - 3y) = -12.8 c. 2x... Elige el método más adecuado para resolver los siguientes sistemas de ecuaciones: a. x - 4y + 5 = 2y + 3x - 3 6x = 1 + 5y b. 2.8x - 1.7y = 8.9 3.2(x - 3y) = -12.8 c. 2x + y/4 = 5 -3(x - 1) + 13 = 2(y + 1) d. 2(5x - 3) + 2y = 0 -3(x - y) = -(x + 8) e. 2x - y + 3(x - y) = -4 5(x - 3y) + 2y - 3(3x - 2y) = -7 Read more

Steps to Solve

1. Simplify the equations First, simplify each system of equations to a standard form (e.g., $ax + by = c$). This will make it easier to determine the best method for solving each system.

2. Analyze system a First equation: $x - 4y + 5 = 2y + 3x - 3 \implies -2x - 6y = -8 \implies x + 3y = 4$. Second equation: $6x = 1 + 5y \implies 6x - 5y = 1$. The elimination or substitution methods would be suitable since the equations can be easily rearranged.

3. Analyze system b First equation: $2.8x - 1.7y = 8.9$. Second equation: $3.2(x - 3y) = -12.8 \implies 3.2x - 9.6y = -12.8$. The elimination method looks good here since we can easily eliminate $x$ multiplying the first equation by $-3.2$ and the second equation by $2.8$

4. Analyze system c First equation: $2x + \frac{y}{4} = 5$. Second equation: $-3(x - 1) + 13 = 2(y + 1) \implies -3x + 3 + 13 = 2y + 2 \implies -3x - 2y = -14 \implies 3x + 2y = 14$. The substitution or elimination methods are appropriate.

5. Analyze system d First equation: $2(5x - 3) + 2y = 0 \implies 10x - 6 + 2y = 0 \implies 10x + 2y = 6 \implies 5x + y = 3$. Second equation: $-3(x - y) = -(x + 8) \implies -3x + 3y = -x - 8 \implies -2x + 3y = -8$. The substitution or elimination methods are suitable.

6. Analyze system e First equation: $2x - y + 3(x - y) = -4 \implies 2x - y + 3x - 3y = -4 \implies 5x - 4y = -4$. Second equation: $5(x - 3y) + 2y - 3(3x - 2y) = -7 \implies 5x - 15y + 2y - 9x + 6y = -7 \implies -4x - 7y = -7$. The substitution or elimination methods are appropriate.