5x-5y-4z=-3 x-y+5z=11 4x-3y-6z=-9

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вопрос

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

Let's start by using the substitution method.

From the first equation, we can solve for x:
5x - 5y - 4z = -3
5x = 5y + 4z - 3
x = (5y + 4z - 3)/5

Now we substitute x into the other two equations:

x - y + 5z = 11
(5y + 4z - 3)/5 - y + 5z = 11
5y + 4z - 3 - 5y + 5z = 55
4z - 3 + 5z = 55
9z - 3 = 55
9z = 58
z = 58/9

Next, we substitute z back into the equation for x:
x = (5y + 4z - 3)/5
x = (5y + 4(58/9) - 3)/5
x = (5y + 232/9 - 3)/5
x = (5y - 9 + 232)/45
x = (5y + 223)/45

Now, we can substitute both x and z into the third equation:

4x - 3y - 6z = -9
4(5y + 223)/45 - 3y - 6(58)/9 = -9
(20y + 892)/45 - 3y - 348/3 = -9
20y + 892 - 135y - 1044 = -405
-115y - 152 = -405
-115y = -253
y = 253/115

Now that we have found the values of y and z, we can substitute them back into the equations for x:

x = (5(253/115) + 223)/45
x = (1265/115 + 223)/45
x = (1265 + 2585)/1035
x = 3850/1035

Therefore, the solution to the system of equations is:
x = 3850/1035
y = 253/115
z = 58/9