Question

X+y+z=101 5x=7y 0,75y=6z x=? y=? z=?

Answer 1

X=101-y-z
X=7/5y
Y=6/0.75z
101-8z-z=11,2z
101=20,2z
Z=5
Y=40
X=101-45
X=56

Answer 2

Ответ:

x+y+z=101

x=7y/5

z=0.75y/6

7y/5 + y + 0.75y/6 = 101, умножаем на 30

42y+y+3.75y=3030

75.75y=3030

y=40

x=7y/5=56

z=7.5y/6=5

Пошаговое объяснение:

Answer 3

To solve this system of linear equations for x, y, and z, you can use the following steps:

1. Start with the equations you have:

   a) x + y + z = 101 b) 5x = 7y c) 0.75y = 6z

2. Let's solve equation (c) for y:

   0.75y = 6z y = (6z) / 0.75

   Simplify:

   y = 8z

3. Now, substitute the expression for y from equation (b) and (c) into equation (a):

   x + 5x + 8z = 101

4. Combine like terms:

   6x + 8z = 101

5. Next, isolate x:

   6x = 101 - 8z

6. Divide both sides by 6:

   x = (101 - 8z) / 6

Now, you have expressions for x and y in terms of z. You can substitute these into the equations to find the values of x, y, and z:

Using equation (b):

5x = 7y 5((101 - 8z) / 6) = 7(8z)

Now, solve for z:

40z + 5(101 - 8z) = 56z

Distribute:

40z + 505 - 40z = 56z

The z terms cancel out:

505 = 56z

Divide by 56:

z = 505 / 56

z ≈ 9.0179 (rounded to four decimal places)

Now that you have the value of z, you can find x and y:

x = (101 - 8z) / 6 x = (101 - 8 * 9.0179) / 6 x ≈ 14.3032 (rounded to four decimal places)

And since y = 8z:

y = 8 * 9.0179 y ≈ 72.1432 (rounded to four decimal places)

So, the approximate values of x, y, and z are:

x ≈ 14.3032 y ≈ 72.1432 z ≈ 9.0179