Questions: Solve the system of equations by using a table. y=3x-4 y=-2x+11 x y -3 0 1 3 6

Solve the system of equations by using a table. y=3x-4 y=-2x+11 x y -3 0 1 3 6
Transcript text: Solve the system of equations by using a table. \[ \begin{array}{c} y=3 x-4 \\ y=-2 x+11 \end{array} \] \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline-3 & \\ \hline 0 & \\ \hline 1 & \\ \hline 3 & \\ \hline 6 & \\ \hline \end{tabular}
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Solution

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Paso 1: Evaluar las ecuaciones

Calculamos \( y \) para cada valor de \( x \) utilizando las ecuaciones \( y = 3x - 4 \) y \( y = -2x + 11 \).

Paso 2: Llenar la tabla

Para \( x = -3 \):

  • \( y_1 = 3(-3) - 4 = -13 \)
  • \( y_2 = -2(-3) + 11 = 17 \)

Para \( x = 0 \):

  • \( y_1 = 3(0) - 4 = -4 \)
  • \( y_2 = -2(0) + 11 = 11 \)

Para \( x = 1 \):

  • \( y_1 = 3(1) - 4 = -1 \)
  • \( y_2 = -2(1) + 11 = 9 \)

Para \( x = 3 \):

  • \( y_1 = 3(3) - 4 = 5 \)
  • \( y_2 = -2(3) + 11 = 5 \)

Para \( x = 6 \):

  • \( y_1 = 3(6) - 4 = 14 \)
  • \( y_2 = -2(6) + 11 = -1 \)
Paso 3: Comparar los resultados

Comparamos los valores de \( y_1 \) y \( y_2 \) para encontrar el punto de intersección:

  • Para \( x = 3 \), \( y_1 = 5 \) y \( y_2 = 5 \), lo que indica que \( (3, 5) \) es la solución del sistema de ecuaciones.
Respuesta Final

\(\boxed{(3, 5)}\)

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