Question

por favor me ajude Eu não estou conseguindo responder o 22,23

Answer 1

Questão 22:

$\left \{ {{x + y = 25} \atop {5x + 8y = 170}} \right.$ 

Pela regra de Cramer:

$\left[\begin{array}{ccc}1&1\\5&8\\\end{array}\right] x \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}25\\170\\\end{array}\right]$

$Det A \left[\begin{array}{ccc}1&1\\5&8\\\end{array}\right] = (1 * 8) - (5 * 1) = 3$

Para x:

$Det B \left[\begin{array}{ccc}25&1\\170&8\\\end{array}\right] = (25 * 8) - (170 * 1) = 30$

$x = \frac{Det B}{Det A}$

$x = \frac{30}{3}$

x = 10

Para y:

$Det C \left[\begin{array}{ccc}1&25\\5&170\\\end{array}\right] = (1 * 170) - (5 * 25) = 45$

$y = \frac{Det C}{Det A}$

$y = \frac{45}{3}$

y = 15

Portanto:
x = 10 cubos de 5 cm
y = 15 cubos de 8 cm

Vamos verificar: 

$\left \{ {{x + y = 25} \atop {5x + 8y = 170}} \right.$

10 + 15 = 25
25 = 25 [OK]

5 × 10 + 8 × 15 = 170
50 + 120 = 170
170 = 170 [OK]


Questão 23:

$\left \{ {{x + y = 300} \atop {x + \frac{y}{2} = 180}} \right.$

Porém, dividir por 2 é o mesmo que multiplicar por 0,5, Logo:

$\left \{ {{x + y = 300} \atop {x + 0,5y = 180}} \right.$

Pela regra de Cramer:

$\left[\begin{array}{ccc}1&1\\1&0,5\\\end{array}\right] x \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}300\\180\\\end{array}\right]$

$Det A \left[\begin{array}{ccc}1&1\\1&0,5\\\end{array}\right] = (1 * 0,5) - (1 * 1) = -0,5$

Para x:

$Det B \left[\begin{array}{ccc}300&1\\180&0,5\\\end{array}\right] = (300 * 0,5) - (180 * 1) = -30$

$x = \frac{Det B}{Det A}$

$x = \frac{-30}{-0,5}$

x = 60

Para y:

$Det C\left[\begin{array}{ccc}300&1\\180&0,5\\\end{array}\right] = (300 * 0,5) - (180 * 1) = -30$

$y = \frac{Det C}{Det A}$

$y = \frac{-120}{-0,5}$

y = 240

Portanto:
y = 240g (peso do suco)
x = 60g ( peso do copo)

Vamos verificar: 

$\left \{ {{x + y = 300} \atop {x + \frac{y}{2} = 180}} \right.$

60 + 240 = 300
300 = 300 [OK]

60 + $\frac{240}{2}$ = 180
60 + 120 = 180
180 = 180 [OK]