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jolli1 [7]
3 years ago
12

What is 3x+2y=-13 3x+4y=1

Mathematics
1 answer:
Zepler [3.9K]3 years ago
4 0

Answer:

The values are

x = -25/9 = -2 7/9

y = 7/3 = 2 1/3

Step-by-step explanation:

3x + 2y = -13 --------eqn 1

3x + 4y = 1-------------eqn2

Using eqn 2 to get the value of y

3x + 4y = 1

4y = 1 - 3x

Dividing both sides by 4,to get y

4y/4 =( 1 -3x) / 4

y = (1 - 3x) / 4

Since we've gotten the value for y, substitute the value into eqn 1

3x + 2y = -13

3x + 2(3x - 1)/4 = -13

Opening the bracket

3x + (6x - 2)/4 = -13

LCM = 4

(12x + 6x - 2) / 4 = -13

18x - 2 / 4 = -13

Then we cross multiply

18x - 2 = -13 * 4

18x - 2 = - 52

18x = -52 + 2

18x = -50

Divide both sides by 18, to get the value of x

18x/18 = -50/18

x = -25/9

or x = -2 7/9

The value of x is now known, so let's go back to eqn 2

Substitute x = - 25/9

3x + 4y = 1

3(-25/9) + 4y = 1

Open the bracket

-75/9 + 4y = 1

Make y the subject of the formula

4y = 1 + 75/9

LCM = 9

4y = (9 + 75)/ 9

4y = 84/9

To get y, divide both sides by 4

4y/4 = 84/9 / 4/1

y =

Note : when division changes to multiplication, it always be in its reciprocal form

y = 84/9 / 1/4

y = 84 * 1 / 9 *4

y = 84/ 36

y = 7/3

Or

y = 2 1/3

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La barbería El Caleño, tiene en promedio 120 clientes a la semana a
Luba_88 [7]

Queremos maximizar el precio de tal forma que los ingresos no disminuyan.

Ese maximo precio es: $14,040.6

Sabemos que actualmente el precio es:

p = $6,000

El número de clientes es:

C = 120

Actualmente los ingresos son el producto de esos dos números, es decir:

ingresos = $6,000*120 = $720,000

Ahora sabemos que por cada incremento de $700 en el precio, el número de clientes decrece en 10.

Entonces podemos escribir el número de clientes como una ecuación lineal.

C(p) = a*p + b

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($6,000, 120)

($6,700, 110)

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C($6,000) = 120 = (-10/$700)*$6,000 + b

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Entonces la ecuación lineal es:

C(p) = (-10/$700)*p + 205.71

Los ingresos serán dados por:

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Y queremos maximizar p de tal forma que esto sea igual a lo que obtuvimos antes:

(-10/$700)*p^2 + 205.71*p = $720,000

Entonces debemos resolver la ecuación cuadratica:

(-10/$700)*p^2 + 205.71*p - $720,000 = 0.

Las soluciones son dadas por la formula de Bhaskara.

p = \frac{-205.71 \pm \sqrt{(205.71)^2 - 4*(-10/\$ 700)*\$ 720,000} }{2*(-10/\$ 700)} \\\\p = \frac{-205.71 \pm 195.45}{(-20/\$ 700)}

La solución de maximo valor es:

p = (-205.71 - 195.45)/(-20/$700) = $14,040.6

Sí quieres aprender más, puedes leer.

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