5х+y-3z= -2 4x+3y+2z= 16 2x-3y+z= 17

Предыдущий
вопрос Следующий
вопрос

To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution in this case.

From the first equation, we have:
5x + y - 3z = -2
y = -5x + 3z - 2

Now substitute y into the second and third equations:

4x + 3(-5x + 3z - 2) + 2z = 16
4x - 15x + 9z - 6 + 2z = 16
-11x + 11z = 22
x - z = -2 (1)

2x - 3(-5x + 3z - 2) + z = 17
2x + 15x - 9z + 6 + z = 17
17x - 8z = 11
17x = 8z + 11
x = (8/17)z + 11/17 (2)

Substitute (2) into equation (1):

(8/17)z + 2 - z = -2
(8/17)z - z = -2 - 2
-(9/17)z = -4
z = -4*(-17/9)
z = 68/9

Now, substitute z back into equation (2) to solve for x:

x = (8/17)*(68/9) + 11/17
x = 32/3

Finally, substitute x and z back into the equation y = -5x + 3z - 2 to solve for y:

y = -5(32/3) + 3(68/9) - 2
y = -160/3 + 204/9 - 2
y = -160/3 + 68/3 - 2
y = -92/3 - 6
y = -104/3

Therefore, the solution to the system of equations is:
x = 32/3, y = -104/3, z = 68/9.