Tìm x; y; z biết

To solve this system of equations, we can start by simplifying the first equation:

x + 1/3 = y + 2/-4 = z - 3/5

We can rewrite the second fraction as a negative fraction:

x + 1/3 = y - 1/2 = z - 3/5

Now, let's solve for x in terms of y and z:

x = y - 1/2
x = z - 3/5

Now, substitute these expressions for x into the second equation:

3(y - 1/2) + 2y + 4(z - 3/5) = 27

Distribute and simplify:

3y - 3/2 + 2y + 4z - 12/5 = 27

Combine like terms:

5y - 3/2 + 4z - 12/5 = 27

To get rid of the fractions, we can multiply every term by 10:

10(5y - 3/2) + 10(4z - 12/5) = 10(27)

50y - 15 + 40z - 24 = 270

Combine like terms:

50y + 40z - 39 = 270

Now, let's solve for y in terms of z:

50y = 270 - 40z + 39
50y = 309 - 40z
y = (309 - 40z)/50
y = (309 - 8z)/10

Now, substitute these expressions for y and x into the first equation:

x + 1/3 = (309 - 8z)/10 - 1/2 = z - 3/5

To get rid of the fractions, we can multiply every term by 30:

30x + 10 = 3(309 - 8z) - 15(1/2) = 30z - 18

Distribute and simplify:

30x + 10 = 927 - 24z - 15/2 = 30z - 18

Combine like terms:

30x + 10 = 927 - 24z - 7.5 = 30z - 18

Combine like terms:

30x = 927 - 24z - 7.5 - 10 = 30z - 18 - 10

30x = 909.5 - 24z = 30z - 28

Now, let's solve for x in terms of z:

30x = 909.5 - 24z
x = (909.5 - 24z)/30
x = (303.17 - 8z)/10

So, the solution to the system of equations is x = (303.17 - 8z)/10, y = (309 - 8z)/10, and z = z.