Mathematics, 29.03.2020 21:55, bah103

Solve the system
2x+2y+z=-2
-x-2y+2z=-5
2x+4y+z=0

Answers: 1

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Answers

answered: janyiareese12

The values of (x,y,z) are (3,-1,-2) , if the given are equations 2x+2y+z=- 2 , -x-2y+2z=-5 and 2x+4y+z=0 .

Step-by-step explanation:

The given is,

2x+2y+z=- 2 .......................................(1)

-x-2y+2z=-5 ......................................(2)

2x+4y+z=0 .........................................(3)

Step:1

Equation (2) is multiplied by -1 ( Eqn(2) × -1 )

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

Subtract the equation (1) and (4)

2x+2y+z=- 2

x+2y-2z=5

( - )

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

x+3z=-7 ......................(5)

Step:2

Equation (2) is multiplied by -2 ( Eqn(2) × -2)

2x+4y-4z=10 ........................(6)

Subtract equation (6) and (3),

2x+4y-4z=10

2x+4y+z=0

( - )

(2x-2x)+(4y-4y)+(-4z-z)= (10-0)

-5z=10

$z = - \frac{10}{5}$

z = -2

From the equation (5),

x+3z=-7

x+(3)(-2)=-7

x = -7+6

x = -1

From equation (1),

2x+2y+z=- 2

Substitute x and z values,

(2)(-1)+2y+(-2)=-2

2y - 4=2

2y=4-2

2y=2

$y=\frac{2}{2}$

y = 1

Step:3

Check for solution,

-x-2y+2z=-5

Substitute x,y and z values,

-(-1)-(2)(1)+(2)(-2)=-5

1-2-4=-5

-5 = -5

Result:

The values of (x,y,z) are (3,-1,-2) , if the given are equations 2x+2y+z=- 2 , -x-2y+2z=-5 and 2x+4y+z=0 .

answered: Guest

i suppose it should be (y=2x-5)

step-by-step explanation:

answered: Guest

hence, the required result is $b-a=\left[\begin{array}{ccc}1& 1& -2\\1& 1& -2\\1& 1& -2\end{array}\right]$

step-by-step explanation:

suppose we have two matrices a and b

we will assume the two matrices

$a=\left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right]$

$b=\left[\begin{array}{ccc}2& 3& 1\\5& 6& 4\\8& 9& 7\end{array}\right]$

we have to compute b-a which means subtracting corresponding elements of a from b.

$b=\left[\begin{array}{ccc}2& 3& 1\\5& 6& 4\\8& 9& 7\end{array}\right]$ - $a=\left[\begin{array}{ccc}1& 2& 3\\4& 5& 6\\7& 8& 9\end{array}\right]$

$b-a=\left[\begin{array}{ccc}1& 1& -2\\1& 1& -2\\1& 1& -2\end{array}\right]$

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Solve the system
2x+2y+z=-2
-x-2y+2z=-5
2x+4y+z=0...