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attashe74 [19]
3 years ago
8

What is 18+6x=41+4x,x

Mathematics
1 answer:
Novay_Z [31]3 years ago
4 0

Answer:

x=11.5

Step-by-step explanation:

18+6x=41+4x

Subtract 4x from each side

18+6x-4x=41+4x-4x

18+2x = 41

Subtract 18 from each side

18-18 +2x = 41-18

2x =23

2x/2 = 23/2

x =11.5

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The given system of equations in augmented matrix form is

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If you need to solve this, first get the matrix in RREF:

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\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&11&5&-13&37\\0&19&10&4&-10\end{array}\right]

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\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&-91&153&-823\\0&0&-164&132&-1052\end{array}\right]

  • Add 164(row 3) to -91(row 4):

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  • Multiply row 4 by 1/13080:

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  • Multiply row 3 by -1/91:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&-6&8&-58\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

  • Add 6(row 3) and -8(row 4) to row 2:

\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&5&0&0&-10\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

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\left[\begin{array}{cccc|c}3&2&-4&2&-23\\0&1&0&0&-2\\0&0&1&0&4\\0&0&0&1&-3\end{array}\right]

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