Pregunta
6) \( \left\{\begin{array}{l}y=-5 \\ 8 x+5 y=-17\end{array}\right. \)
Ask by Stephens Zimmerman. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The solution is \( x = 1 \) and \( y = -5 \).
Solución
To solve the system of equations:
\[
\begin{cases}
y = -5 \\
8x + 5y = -17
\end{cases}
\]
**Step 1:** Substitute the value of \( y \) from the first equation into the second equation.
Given:
\[
y = -5
\]
Substitute into the second equation:
\[
8x + 5(-5) = -17
\]
**Step 2:** Simplify the equation.
\[
8x - 25 = -17
\]
**Step 3:** Solve for \( x \).
\[
8x = -17 + 25 \\
8x = 8 \\
x = \frac{8}{8} \\
x = 1
\]
**Solution:**
\[
x = 1 \quad \text{and} \quad y = -5
\]
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Simplifique esta solución Bonus Knowledge
To solve this system of equations, start by substituting the value of \(y\) from the first equation into the second equation. Since \(y = -5\), plug this into \(8x + 5y = -17\): \[ 8x + 5(-5) = -17 \\ 8x - 25 = -17 \\ 8x = 8 \\ x = 1 \] Thus, the solution to the system is \(x = 1\) and \(y = -5\), or the point \((1, -5)\). When working with systems of equations, it's great to check your solution by substituting both values back into the original equations to ensure they hold true. In this case: 1. For \(y = -5\), it is already set. 2. Plugging \(x = 1\) and \(y = -5\) into the second equation, \(8(1) + 5(-5) = 8 - 25 = -17\), confirms our solution is indeed correct!
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