Question

The system of equations X-4y+72 = 12, 3x+8y-2z = 10, 26 z-8y = 6​

Answer 1

Answer:

this is from linear equation

Explanation:

X-4y+72 = 12, 3x+8y-2z = 10, 26 z-8y = 6

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Answer 2

Given:

We are given three equations each in two variable

x - 4y + 72 = 12   (i)

3x + 8y - 2z = 10 (ii)

26z - 8y = 6​        (iii)

To find:

The value of x,y,z

Solution:

In this question, we will start by substituting the value of one variable of an equation into the second equation.

We will start with simplifying the first equation

x- 4y + 72 = 12

x = 12 - 4y -72

Now we will substitute the value of (x) into the second equation (ii)

3x + 8y - 2z = 10

3(12 - 4y - 72 ) +8y-2z = 10

36 - 12y - 216 + 8y - 2z = 10

-186 -4y - 2z = 10

-196 - 2z  = 4y

-196 - 2z / 4 = y

y = -196 - 2z / 4

We will now simplify the third equation.(iii)

26z - 8y = 6​

13z -4y = 3

13z - 3 = 4y

Now we will substitute the value of y into the simplified equation (iii)

13z - 3 = 4y

13z - 3 = 4(-196 - 2z / 4 )

13z - 3 = -196 - 2z

15z = - 193

z = - 193 / 15

Putting the value of z as - 193 / 15 in the third equation (iii)

26z - 8y = 6​

13z -4y = 3

13z - 3 = 4y

13(- 193 / 15)- 3 = 4y

-2509/15 - 3 = 4y

-2509 - 45 /15 = 4y

-2509 - 45 / 60 = y

- 2464/ 60 = y

-66/15 = y

Now substituting the value of x into first equation

x - 4y + 72 = 12   (i)

x - 4(-66/15) + 72 = 12

x + 264/15 + 72 = 12

x = 12 - 72 - 264/15

x =  - 60 - (88/5)

x = - 388/ 5