Determine whether the system is consistent. 2) x1 + x2 + x3=7 x1-x2+ 2x3-7 2x1 3x3 15 a) no b) yes

A) No

Step-by-step explanation:

A system is consitent if it has an solution, or many solutions.

If it ends at a division by 0, or 0 = constant(different than 0), the system is inconsistent.

Let's solve this system

x1 + x2 + x3 = 7

x1 - x2 + 2x3 = 7

2x1 + 3x3 = 15

From the first equation

x1 + x2 + x3 = 7

x3 = 7 - x1 - x2

Replacing in the other equations:

In the second

x1 - x2 + 2x3 = 7

x1 - x2 + 2(7 - x1 - x2) = 7

x1 - x2 + 14 - 2x1 - 2x2 = 7

-x1 - 3x2 = -7

In the third

2x1 + 3x3 = 15

2x1 + 3(7 - x1 - x2) = 15

2x1 + 21 - 3x1 - 3x2 = 15

-x1 - 3x2 = - 6

So we have the following system now:

-x1 - 3x2 = -7

-x1 - 3x2 = - 6

Multiplying the second equation by -1, and adding both equations

-x1 - 3x2 = -7

x1 + 3x2 = 6

0 = -1

This is something that is false, so the system is inconsistent.

The correct answer is:

A) No

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