X1+x2-x3=2-2x1+x2+x3=3x1+x2+x3=6

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вопрос

To solve this system of equations, we can use the method of substitution.

From the first equation, we can isolate x1:
x1 = 2-x2+x3

Now substitute this expression for x1 into the second equation:
2(2-x2+x3) + x2 + x3 = 3
Expanding the brackets:
4 - 2x2 + 2x3 + x2 + x3 = 3
Combining like terms:
4 - x2 + 3x3 = 3
Rearranging terms:
x2 - 3x3 = 1 (Equation 4)

Now substitute the expression for x1 into the third equation:
3(2-x2+x3) + x2 + x3 = 6
Expanding:
6 - 3x2 + 3x3 + x2 + x3 = 6
Combining like terms:
-x2 + 4x3 = 0
Rearranging terms:
x2 = 4x3 (Equation 5)

Now substitute equation 5 into equation 4:
4x3 - 3x3 = 1
x3 = 1

Substitute x3 back into equation 5 to find x2:
x2 = 4(1) = 4

Finally, substitute x2 and x3 back into the expression for x1:
x1 = 2 - 4 + 1 = -1

Therefore, the solution to the system of equations is:
x1 = -1, x2 = 4, x3 = 1