Mathematics, 05.07.2019 08:30 GiuliAzevedo

Solve the system, show each step. x + y + z = -4 -x + 2y + 3z = 3 x - 4y - 2z = -15

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Answer from: hannahcolleen4895

The solution of the system of equations is $x=\frac{-53}{11}$ , $y=\frac{47}{11}$ and $z=\frac{-38}{11}$ .

Explanation:

The given equations are,

x+y+z=-4 ..... (1)

-x+2y+3z=3 ..... (2)

x-4y-2z=-15 ...... (3)

From equation we get,

x=-4-y-z

Put this value in equation (4) and (5).

-(-4-y-z)+2y+3z=3

3y+4z=-1 .... (4)

(-4-y-z)-4y-2z=-15

-5y-3z=-11 .....(5)

Use elimination method to solve the equations (4) and (5).

Multiply equation (4) by 3 and equation (5) by 4, then add both equations as shown in figure,

-11y=-47

$y=\frac{47}{11}$

Put this value in equation (4).

$3(\frac{47}{11})+4z=-1$

$4z=-1-\frac{141}{11}$

$4z=\frac{-11-141}{11}$

$z=\frac{-152}{11\times 4}$

$z=\frac{-38}{11}$

Put $y=\frac{47}{11}$ and $z=\frac{-38}{11}$ in equation (1).

$x+\frac{47}{11}+\frac{-38}{11}=-4$

$x+\frac{9}{11}=-4$

$x=\frac{-44-9}{11}$

$x=\frac{-53}{11}$

Therefore, the The solution of the system of equations is $x=\frac{-53}{11}$ , $y=\frac{47}{11}$ and $z=\frac{-38}{11}$ .

Solve the system, show each step. x + y + z = -4 -x + 2y + 3z = 3 x - 4y - 2z = -15

Answer from: hayesgenniferozslxr

The given equations are

x + y + z = -4

-x + 2 y + 3 z = 3

x - 4 y - 2 z = -15

Writing in matrix form

A= 1 1 1 X= x B= -4

-1 2 3 y 3 ⇒A,X,B are in matrix form.

1 -4 -2 z -15

i.e Ax=B

x = $A^{-1}$ B

but , $A^{-1}$ =Adj.(A)/Determinant A

Determinant of A= 1(-4+12) -1(2-3)+1(4-2)=8+1+2=11

To find Adjoint of matrix A, we will find the cofactor of A and then it's transpose.

$a_{11}$ =-4+12=8, $a_{12}=-[2-3]=1,$

$,a_{13}=4-2=2,\\,a_{21}=-[-2+4]=-2\\,a_{22}=-2-1=-3,\\a_{23}=-[-4-1]=5,\\a_{31}=[3-2]=1\\,a_{32}=-[3+1]=-4\\,a_{33}=2+1=3$

Now taking cofactor, and getting the adjoint

Adjoint (A)= 8 -2 1

1 - 3 -4

2 5 3

Adjoint(A). B= -53

-38

$\frac{Adjoint (A)\times B}{Determinant A}$ = -53/11

47/11

-38/11

So, solution set is , x=-53/11, y=47/11, z=-38/11

Answer from: Quest

0=6x+2y+10 is equivalent to the simplified form: y= -3x - 5• parallel lines always have the same slope, different y intercept knowing this, we can say the slope, or m of the line parallel to y= -3x - 5 is -3.m= -3 hope this could !
Find the slope of the line parallel to each given line

Find the slope of the line parallel to each given line

Answer from: Quest

drop out of school or go to quizlet, quizlet is better

step-by-step explanation:

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