Question
Asked Sep 9, 2019
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Solve the following system of equations:
2x + 3y + z = 15
x + y + z = 8
3x + 2y - 3z = -4

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Expert Answer

Step 1

Given,

          The following system of equations:

2x 3y z
15
(i)
(ii)
(iii)
= 8
x y z
3x2y 3z
-4
help_outline

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2x 3y z 15 (i) (ii) (iii) = 8 x y z 3x2y 3z -4

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Step 2

Solving the above system of equation by the elimination method

(i) 2(ii2x + 3y z 2(x + y + z) = 15 2 x 8
2x 3y z - 2x - 2y - 2z = 15 - 16
(iv)
y-z-1
(iii 3(ii
3x 2y-3z - 3(x + y + z)
-4 3 x 8
=
3x 2y- 3z 3x - 3y - 3z = -4 - 24
(v)
-y6z-28
Adding the equation (iv) and (v), we get
(iv)(v)yz (-y6z-1+ (-28)
y-z-y 6z = -29
-7z -29
29
Z
7
help_outline

Image Transcriptionclose

(i) 2(ii2x + 3y z 2(x + y + z) = 15 2 x 8 2x 3y z - 2x - 2y - 2z = 15 - 16 (iv) y-z-1 (iii 3(ii 3x 2y-3z - 3(x + y + z) -4 3 x 8 = 3x 2y- 3z 3x - 3y - 3z = -4 - 24 (v) -y6z-28 Adding the equation (iv) and (v), we get (iv)(v)yz (-y6z-1+ (-28) y-z-y 6z = -29 -7z -29 29 Z 7

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Step 3

Now, putting the value of z ...

29
(iv)y
-1
7
29
1
y
7
29-7
y
7
22
y=
7
help_outline

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29 (iv)y -1 7 29 1 y 7 29-7 y 7 22 y= 7

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Tagged in

Math

Calculus