Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.

1 answer:

4 0

Using Gaussian elimination:
x + y + z = 9 / * ( - 2 ) / ( - 1 ) ( we will multiply by - 2 and add to the 2nd 2 x - 3 y + 4 z = 7 equation and multiply by - 1 and add to the 3rd equation )
x - 4 y + 3 z = - 2
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x + y + z = 9
- 5 y + 2 z = - 11 / * ( - 1 )
- 5 y + 2 z = - 11
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x + y + z = 9
- 5 y + 2 z = - 11
0 z = 0
There are infinitely many solutions to the system of equations.
z = t,
- 5 y + 2 t = - 11
5 y = 11 + 2 t
y = ( 11 + 2 t ) / 2
x + ( 11 + 2 t ) / 2 + t = 9 / * 2
2 x + 11 + 2 t + 2 t = 18
2 x = 18 - 11 - 4 t
x = ( 7 - 4 t ) / 2
( x, y , z ) = ( (7 - 4 t ) / 2, ( 11 + 2 t ) / 2, t )

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2(a³+b²+11)+1(3+a³+b+11)

Ann [662]

Answer:

$2(a^3+b^2+11)+1(3+a^3+b+11)=3a^3+2b^2+b+36$

Step-by-step explanation:

I assume that you need simplification of the given expression.

The given expression is:

$2(a^3+b^2+11)+1(3+a^3+b+11)$

Using distributive property and multiplying 2 inside the parenthesis and 1 inside the other parenthesis. This gives,

$2(a^3+b^2+11)=2\times a^3+2\times b^2+2\times 11\\2(a^3+b^2+11)=2a^3+2b^2+22\\\\1(3+a^3+b+11)=1\times 3+1\times a^3+1\times b+1\times 11\\1(3+a^3+b+11)=3+a^3+b+11=a^3+b+14$