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2 years ago

Solve the system by substitution -x - y - z = -8 -4x + 4y + 5z = 7 2x + 2z = 4

Mathematics

2 answers:

zhuklara [117]2 years ago

7 0

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

$-4(2-z)+4y+5z=7\\\\\Rightarrow -8+4z+4\times6+5z=7\\\\\Rightarrow 9z+16=7\\\\\Rightarrow 9z=-9\\\\\Rightarrow z=-\dfrac{9}{9}\\\\\Rightarrow z=-1.$

From equation (iii), we get

$2x+2(-1)=4\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.$

Thus, the required solution of the given system is

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

gulaghasi [49]2 years ago

5 0

Answer: 14

Step-by-step explanation:

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