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mafiozo [28]
3 years ago
10

Explain how you would estimate to subtract 189 from 643

Mathematics
1 answer:
Dima020 [189]3 years ago
5 0
I would just round up to 200 and then subtract twelve or just subtract 200 what ever way u prefer. 
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Answer:

The system has infinite solutions described in the set \{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{cccc}-1&-1&-1&4\\2&1&0&2\end{array}\right].

We apply row operations:

1. We add the first row to the second row twice and obtain the matrix \left[\begin{array}{cccc}-1&-1&-1&4\\0&-1&-2&10\end{array}\right]

2. multiply by -1 the rows of the previous matrix and obtain the matrix \left[\begin{array}{cccc}1&1&1&-4\\0&1&2&-10\end{array}\right] that is the reduced echelon form of the matrix associated to the system.

Now we aply backward substitution:

1. Observe that the reduced echelon form has a free variable, then the system has infinite solutions.

2.

x_2+2x_3=-10\\x_2=-10-2x_3

3.

x_1+x_2+x_3=-4\\x_1-10-2x_3+x_3=-4\\x_1-x_3=-4+10\\x_1=6+x_3.

Then the set of solutions is \{(x_1,x_2,x_3)=(6+s1, -10-2s1,s1): s1\in\mathbb{R}\}

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