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Answer
La solución es \( x = -2 \) y \( y = -3 \).
Solution
Para resolver el sistema de ecuaciones:
1. \( 3x + y = -9 \)
2. \( 4x - 3y = 1 \)
**Paso 1: Despejar una variable en una de las ecuaciones.**
Vamos a despejar \( y \) de la primera ecuación.
\[ 3x + y = -9 \]
\[ y = -9 - 3x \]
**Paso 2: Sustituir la expresión obtenida en la segunda ecuación.**
Sustituyendo \( y = -9 - 3x \) en la segunda ecuación:
\[ 4x - 3(-9 - 3x) = 1 \]
\[ 4x + 27 + 9x = 1 \]
\[ 13x + 27 = 1 \]
**Paso 3: Resolver para \( x \).**
\[ 13x = 1 - 27 \]
\[ 13x = -26 \]
\[ x = \frac{-26}{13} \]
\[ x = -2 \]
**Paso 4: Encontrar el valor de \( y \) usando el valor de \( x \).**
Usando la expresión \( y = -9 - 3x \):
\[ y = -9 - 3(-2) \]
\[ y = -9 + 6 \]
\[ y = -3 \]
**Conclusión:**
La solución del sistema es:
\[ x = -2 \]
\[ y = -3 \]
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Simplify this solution Bonus Knowledge
To solve this system of equations, you can use the elimination or substitution method. Let’s opt for the substitution method. First, solve the first equation for \( y \): \( y = -9 - 3x \). Now, substitute this expression for \( y \) in the second equation \( 4x - 3(-9 - 3x) = 1 \). After simplifying and solving for \( x \), you'll find the value of \( x \), and then you can plug it back to find \( y \). After solving, you'll get \( x = 2 \) and \( y = -15 \). So, your solution is \( (2, -15) \). You can also check your solution by plugging these values back into the original equations to ensure they both hold true!
