How do you solve the system 3x-y z=5, x 3y 3z=-6, and x 4y-2x=12?

1 answer:

8 0

3x - y + z = 5 . . . (1)
x + 3y + 3z = -6 . . . (2)
x + 4y - 2z = 12 . . . (3)

From (2), x = -6 - 3y - 3z . . . (4)
Substituting for x in (1) and (3) gives
3(-6 - 3y - 3z) - y + z = 5 => -18 - 9y - 9z - y + z = 5 => -10y - 8z = 23 . . (5)
-6 - 3y - 3z + 4y - 2z = 12 => y - 5z = 18 . . . (6)

(6) x 10 => 10y - 50z = 180 . . . (7)
(5) + (7) => -58z = 203
z = 203/-58 = -3.5

From (6), y - 5(-3.5) = 18 => y = 18 - 17.5 = 0.5
From (4), x = -6 - 3(0.5) - 3(-3.5) = -6 - 1.5 + 10.5 = 3

x = 3, y = 0.5, z = -3.5

You might be interested in

Which of the following would NOT work to make a triangle with the two side<br> lengths of 2 and 6?

Roman55 [17]

Answer:

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

If you add 2 and 4, you will get 6. This is the right answer because the only answer that is incorrect is the 4th, it has to equal a minimum of 7, not 6.

4 0

2 years ago

Read 2 more answers

Alexis and Tasha challenged each other to a

Anvisha [2.4K]

Answer:

45 WPM

Step-by-step explanation:

A = 1.2T

54 = 1.2T

T = 45

8 0

3 years ago

Read 2 more answers

A restaurant sells a coffee refill mug for $6.75. Each refill costs $1.25. Last month Keith spent $31.75 on a mug and refills. W

Ronch [10]

The answer is 3975 that the aswer

7 0

3 years ago

Read 2 more answers

1. Two object accumulated a charge of

In-s [12.5K]

Answer:

The magnitude of the electric force between these two objects

will be: 181.274 N.

i.e. F $=181.274$ N

Step-by-step explanation:

Two object accumulated a charge of 4.5 μC and another a charge of 2.8 μC.

q₁ = 4.5 μC = 4.5 × 10⁻⁶ C

q₂ = 2.8 μC = 2.8 × 10⁻⁶ C

separated distance = d = 2.5 cm

Calculating the magnitude of the force between two charged objects using the formula:

$F = \frac{1}{4\pi \epsilon_0}\frac{q_1 q_2}{r^2}$

$=\:\frac{4.5\times \:\:10^{-6}\:\times \:\:2.8\:\times \:\:10^{-6}}{4\:\times \:\left(3.14\right)\:\times \:\left(8.85\times \:10^{-12}\right)\times \left(2.5\times \:\:10^{-2}\right)^2}$

$=\frac{10^{-12}\times \:12.6}{10^{-12}\times \:4\times \:8.85\pi \left(10^{-2}\times \:2.5\right)^2}$ ∵ $4.5\times \:10^{-6}\times \:2.8\times \:10^{-6}=10^{-12}\times \:12.6$

$=\frac{10^{-12}\times \:12.6}{10^{-12}\times \:35.4\pi \left(10^{-2}\times \:2.5\right)^2}$ ∵ $\mathrm{Multiply\:the\:numbers:}\:4\times \:8.85=35.4$