4.7: Sistemas de Ecuaciones- Respuestas a los Ejercicios de Tareas

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Graficando

$(-1,2)$

Sin solución

$(-3,-1)$

$(1,-3)$

$(2,-2)$

$(3,2)$

$(-1,-2)$

$(4,-2)$

$(-3,1)$

$(4,4)$

$(4,-4)$

Sin solución

$(2,-1)$

$(2,3)$

$(-3,1)$

El método de sustitución

$(1, −3)$; consistente; independiente

$(−1, −2)$; consistente; independiente

$(3, 3)$; consistente; independiente

$(−2, −6)$; consistente; independiente

$(−1, 8)$; consistente; independiente

$(1, 7)$; consistente; independiente

$(1, 3)$; consistente; independiente

$(4, −3)$; consistente; independiente

$(0, 3)$; consistente; independiente

$(−4, −1)$; consistente; independiente

$(−3, 3)$; consistente; independiente

$(−1, 0)$; consistente; independiente

$(8, −8)$; consistente; independiente

$(1, −3)$; consistente; independiente

$(−4, 3)$; consistente; independiente

$(0, 2)$; consistente; independiente

$(4, −2)$; consistente; independiente

$(−4, 8)$; consistente; independiente

$(1, −4)$; consistente; independiente

$(2, 5)$; consistente; independiente

El método de adición

$(−2, 4)$; consistente; independiente

Sin solución; inconsistente

$(−3, −5)$; consistente; independiente

$(0, 4)$; consistente; independiente

$(4, 6)$; consistente; independiente

$(0, −4)$; consistente; independiente

$(−1, −2)$; consistente; independiente

$(−8, 9)$; consistente; independiente

$(0, 0)$; consistente; independiente

Infinito número de soluciones; consistente; dependiente

$(2, −2)$; consistente; independiente

$(1, −2)$; consistente; independiente

$(0, 3)$; consistente; independiente

$(1, 2)$; consistente; independiente

$(2, −2)$; consistente; independiente

$(−3, 0)$; consistente; independiente

$(−1, 1)$; consistente; independiente

Aplicaciones con Sistemas de Ecuaciones

$236$adulto,$342$ niño

$130$adultos,$70$ estudiantes

$73$perritos calientes,$58$ hamburguesas

$$12,500 \:@\: 12\%$;$$14,500\: @\: 13\%$

$$2,500\: @\: 10\%$;$$6,500\: @\: 12\%$

$$4,100\: @\: 9.5\%$;$$5,900\: @\: 11\%$

$$1,600\: @\: 4\%$;$$2,400\: @\: 8\%$

$$3,500\: @\: 6\%$;$$5,000\: @\: 3.5\%$

$$6,500\: @\: 8\%$;$$8,500\: @\: 11\%$

$$3,000\: @\: 4.25\%$;$$3,000\: @\: 5.75\%$

$$7,500\: @\: 6.8\%$;$$3,500\: @\: 8.2\%$

$$5,000\: @\: 12\%$;$$11,000\: @\: 8\%$

$30,\: 70$

$40,\: 110$

$100,\: 200$

$10,\: 5$

$21,\: 49$

$2,\: 3$

$1.5,\: 3.5$

$55,\: 20$

$35,\: 63$

$1.2$

$10$

$75$

$63$mph en agua sin gas; tasa de corriente$9$ mph

$5$mph en agua sin gas; tasa de corriente$1$ mph

$\frac{783}{8}$mph en aire quieto; tasa de viento$\frac{113}{8}$ mph

$35$mph en aire quieto; tasa de viento$5$ mph

Sistemas de Tres Ecuaciones Lineales en Tres Variables

$(1, −1, 2)$; consistente; independiente

$(−2, −1, 4)$; consistente; independiente

$(0, 0, 0)$; consistente; independiente

$(0, 0, 0)$; consistente; independiente

$(1, 2, 3)$; consistente; independiente

$(10, 2, 3)$; consistente; independiente

$(3, −2, 1)$; consistente; independiente

$\{(x, y, z)|x + y − z = 0\}$; consistente; dependiente

$\{(x, y, z)|4x + 12y + 16z = 4\}$; consistente; dependiente

$\{(p, q, r)|p + q + r = 1\}$; consistente; dependiente

sin solución; inconsistente

$(2, 3, 1)$; consistente; independiente

$(−25, 18, −25)$; consistente; independiente

$(1, 2, 4)$; consistente; independiente

$(1, −3, −2, −1)$; consistente; independiente

$(7, 4, 5, 6)$; consistente; independiente

Sistemas de Dos Desigualdades Lineales en Dos Variables

si, no, si

si, no, no

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