Question

Solve the system by substitution

-x - y - z = -8
-4x + 4y + 5z = 7
2x + 2z = 4

Answer 1

Answer: 14

Explanation:

Answer 2

Answer: The required solution of the given system is

x = 3, y = 6 and z = -1.

Step-by-step explanation: We are given to solve the following system of equations by the method of substitution :

`-x-y-z=-8~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\-4x+4y+5z=7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\2x+2z=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

From equation (iii), we have

`2x+2z=4\\\\\Rightarrow x+z=2\\\\\Rightarrow x=2-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)`

Substituting the value of x from equation (iv) in equations (i) and (ii), we get

`-(2-z)-y-z=-8\\\\\Rightarrow 2-z+y+z=8\\\\\Rightarrow 2+y=8\\\\\Rightarrow y=8-2\\\\\Rightarrow y=6`

and

`-4(2-z)+4y+5z=7\\\\\Rightarrow -8+4z+4*6+5z=7\\\\\Rightarrow 9z+16=7\\\\\Rightarrow 9z=-9\\\\\Rightarrow z=-(9)/(9)\\\\\Rightarrow z=-1.`

From equation (iii), we get

`2x+2(-1)=4\\\\\Rightarrow 2x=6\\\\\Rightarrow x=(6)/(2)\\\\\Rightarrow x=3.`

Thus, the required solution of the given system is

x = 3, y = 6 and z = -1.