Given that X: Y: z = 2:3:5, and 3x + 4z-2y = 40, find X

Given that X: Y: z = 2:3:5, and 3x + 4z-2y = 40, find X

Let x = 2m, y = 3M, z = 5m
Then 6m + 20m-6m = 40
m=2
∴x=2m=4

Given that the solution of the system of equations {- 3x + y + 3 = 0 / 3x + 2y-6 = O is {x = 4 / 3 / y = 4, try to find the straight line y = 3x-6
The coordinates of the point of intersection with y = 3 / 2 x 3

Equations - 3x + y + 3 = 0
3x+2y-6=0
conversion
y=3x-3 （1）
y=-3/2x+3 （2）
The solution is (4 / 3,4)
Another system of equations
y=3x （3）
y=-3/2x+3 （4）
Four equations represent four straight lines
(2) (4) is the same, (3) for (1) up translation 3 get
So the coordinate of the point of intersection also moves up 3 to get. Y = 7, substituting (4) to get
（-8/3,7）

How many are x, y and Z for solving the cubic equation {x + 2Y + 3Z = 1, y + 2Z + 3x = 2, Z + 2x + 3Y = 3?

x+2y+3z=1（1） y+2z+3x=2（2） z+2x+3y=3（3）
From (1): x = 1-2y-3z (4)
Bring (4) into (2) and (3)
The equations are: 5Y + 7z = 1 - 5z-y = 1
By solving the equations, we can get: y = 2 / 3, z = - 1 / 3
By taking y = 2 / 3 and z = - 1 / 3 into (4), we get the following result:
x=2/3
The results show that the solution of the original ternary linear equations is as follows
x=2/3 y=2/3 z=-1/3