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3 years ago

X+y+z=1

Mathematics

1 answer:

andrezito [222]3 years ago

4 0

Answer: x = 0

y = 2

z = -1

Step-by-step explanation:

The system of equations are

x+y+z=1 - - - - - - - - - - 1

-2x+4y+6z=2 - - - - - - - - - 2

-x+3y-5z=11 - - - - - - - - - 3

Step 1

We would eliminate x by adding equation 1 to equation 3. It becomes

4y -4z = 12 - - - - - - - - - 4

Step 2

We would multiply equation 1 by 2. It becomes

2x + 2y + 2z = 2 - - - - - - - - - 5

We would add equation 2 and equation 5. It becomes

6y + 8z = 4 - - - - - - - - - 6

Step 3

We would multiply equation 4 by 6 and equation 6 by 4. It becomes

24y - 24z = 72 - - - - - - - - 7

24y + 32z = 16 - - - - - - - - 8

We would subtract equation 8 from equation 7. It becomes

-56z = 56

z = -56/56 = -1

Substituting z = -1 into 7, it becomes

24y - 24×-1 = 72

24y + 24 = 72

24y = 72 - 24 = 48

y = 48/24 = 2

Substituting y = 2 and z = -1 into equation 1, it becomes

x + 2 - 1 = 1

x = 1 - 1 = 0

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numerele a, b si c sunt direct proportionale cu 2, 3 si 5. Daca media aritmetica a celor trei numere este egala cu 100, determin

Fynjy0 [20]

Answer:

a = 60

b = 90

c = 150

Step-by-step explanation:

Numerele a, b și c sunt direct proporționale cu 2, 3 și 5.

Unde k este constantă de proporționalitate

a ∝ 2

a = 2k

b ∝ 3

b = 3k

c ∝ 5

c = 5k

Dacă media aritmetică a celor trei numere este egală cu 100, determinați numerele a, b și c

= 2k + 3k + 5k / 3 = 100

= 10k / 3 = 100

Cross Multiply

= 10k = 3 × 100

= 10k = 300

Împărțiți ambele părți la 10

k = 300/10

k = 30

Pentru numărul a

a = 2k

a = 2 × 30

a = 60

Pentru numărul b

b = 3k

b = 3 × 30

b = 90

Pentru numărul c

c = 5k

c = 5 × 30

c = 150

Prin urmare, a = 60, b = 90, c = 150

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3 years ago

To solve a system of inequalities so you can graph it how do you change these two equations into something like the two that are

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Explanation

Problem #2

We must find the solution to the following system of inequalities:

$\begin{gathered} 3x-2y\leq4, \\ x+3y\leq6. \end{gathered}$

(1) We solve for y the first inequality:

$-2y\leq4-3x.$

Now, we multiply both sides of the inequality by (-1), this changes the signs on both sides and inverts the inequality symbol:

$\begin{gathered} 2y\ge-4+3x, \\ y\ge\frac{3}{2}x-2. \end{gathered}$

The solution to this inequality is the set of all the points (x, y) over the line:

$y=\frac{3}{2}x-2.$

This line has:

• slope m = 3/2,

• y-intercept b = -2.

(2) We solve for y the second inequality:

$\begin{gathered} x+3y\leq6, \\ 3y\leq6-x, \\ y\leq-\frac{1}{3}x+2. \end{gathered}$

The solution to this inequality is the set of all the points (x, y) below the line:

$y=-\frac{1}{3}x+2.$

This line has:

• slope m = -1/3,

• y-intercept b = 2.

(3) Plotting the lines of points (1) and (2), and painting the region:

• over the line from point (1),

• and below the line from point (2),

we get the following graph:

Answer

The points that satisfy both inequalities are given by the intersection of the blue and red regions:

8 0

1 year ago