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dolphi86 [110]
2 years ago
13

Solve the system.

Mathematics
1 answer:
Alex777 [14]2 years ago
6 0

Answer:

{x,y,z} = {-18,4,2}

Step-by-step explanation:

Solve equation [2] for the variable  x  

x = -10y + 2z + 18

Plug this in for variable  x  in equation [1]

(-10y+2z+18) + 9y + z = 20

- y + 3z = 2

Plug this in for variable  x  in equation [3]

 3•(-10y+2z+18) + 27y + 2z = 58

   - 3y + 8z = 4

Solve equation [1] for the variable  y  

 y = 3z - 2

Plug this in for variable  y  in equation [3]

  - 3•(3z-2) + 8z = 4

   - z = -2

Solve equation [3] for the variable  z  

 z = 2

By now we know this much :

 x = -10y+2z+18

   y = 3z-2

   z = 2

Use the  z  value to solve for  y  

 y = 3(2)-2 = 4

Use the  y  and  z  values to solve for  x  

 x = -10(4)+2(2)+18 = -18

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Answer: 1

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<em>I hope this helps, and Happy Holidays! :)</em>

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3 years ago
the length of a rectangle is 3cm more than the width. find the length and the width if the perimeter of the rectangle is 98cm.
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The perimeter of a rectangle is <u>length + length + width + width</u>.

We know that the length of a rectangle is 3cm more than its width, which gives us the equation:  (l for length and w for width)

l = 3 + w

We also know that the perimeter of the rectangle is 98cm, which gives us the equation:

98 = 2l + 2w         (equation for perimeter of a rectangle as noted above)

We can divide both sides of this equation by 2 to get:

49 = l + w

Now we'll stick l = 3 + w into the above equation, which gives us:

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which simplifies to 49 = 3 + 2w.

Now we'll subtract 3 from both sides:

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which gives us 46 = 2w.

Dividing both sides by 2 gives us 23 = w.

Substituting w = 23 into the equation l = 3 + w gives us:

l = 3 + 23

l = 26cm.

Let's check our answer.  26cm is 3cm more than 23cm.  26cm + 26cm + 23cm + 23cm gives us 98cm.  The length is 26cm and the width is 23cm.


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