What is the solution of the following system 5x+2y+z=4 x+2z=4 2x+y-z=-1

Let us take the 2nd equation.

x + 2z = 4

x = 4 - 2z

Let us substitute this value of x in equation 1.

5x + 2y + z = 4

5(4-2z) + 2y + z = 4

20 - 10z + 2y + z = 4

2y - 9z + 20 = 4

2y = 9z - 16

y = (9z - 16)/2

Let us substitute this value of y, as well as that of x that we used earlier, in the third equation.

2x + y - z = -1

2(4-2z) + (9z-16)/2 + z = -1

8 - 4z + (9z/2) - 8 + z = -1

Let us multiply both sides of this equation by 2.

16 - 8z + 9z - 16 + 2z = -2

3z = -2

z =

x = 4 - 2z

  = 4 +

  =

y = (9z-16)/2

  = ( - 16)/2

  = ( )/2

  = -22/2

  = -11

Therefore, x = , y = -11, and z = .

1. 2

2. 11

3. 5

4. 6

5. 7

6. 5

7. -1

8. 1

step-by-step explanation: