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Naddika [18.5K]
3 years ago
9

Solve the system. find x,y, and z please show all steps x-y+z=1 x+y+3z=-3 2x-y+2z=0

Mathematics
1 answer:
Mariulka [41]3 years ago
7 0

Solving the system we get, x= -1, y= -2 and z= 0

Step-by-step explanation:

Solving the equations to find x, y and z

x-y+z=1\,\,\,eq(1)\\x+y+3z=-3\,\,\,eq(2)\\2x-y+2z=0\,\,\,eq(3)

Adding eq(1) and eq(2)

x-y+z=1\\x+y+3z=-3\\--------\\2x+4z=-2\,\,\,\,eq(4)\\

Adding eq(2) and eq(3)

x+y+3z=-3\\2x-y+2z=0\\----------\\3x+5z=-3\,\,\,eq(5)

Multiplying eq(4) by 3 and eq(5) by 2

6x+12z=-6\\6x+10z=-6\\-\,\,\,-\,\,\,\,\,\,\,\,\,\,\,\,\,\,+\\----------\\2z=0\\z=0

So, value of z =0

Putting value of z in eq(4)

2x+4z=-2\\2x+4(0)=-2\\2x=-2\\x=-1

So, value of x = -1

Now putting value of z=0 and x =-1 in equation 1

x-y+z=1\\-1-y+0=1\\-y=1+1\\-y=2\\y=-2

So, value of y = -2

So, solving the system we get, x= -1, y= -2 and z= 0

Keywords: Solve the system

Learn more about Solve the system at:

  • brainly.com/question/6075514
  • brainly.com/question/2386054
  • brainly.com/question/7361044

#learnwithBrainly

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1
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<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t   (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

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⇒ z = 2 - cos t - 2sin t

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  \frac{dz}{dt} = \sin t-2cos t

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

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= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}

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8 0
3 years ago
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