It is known that the solutions of the system of equations {3x + 2Y = k 2x-y = K + 1 are opposite to each other, and the value of K is obtained

It is known that the solutions of the system of equations {3x + 2Y = k 2x-y = K + 1 are opposite to each other, and the value of K is obtained

x=-y
3x-2x=k=x
2x+x=k+1=3x=3k
2k=1
k=1/2

Given that the solutions X and y of the equations 3x + 2Y = k5x + 6y = - K are opposite to each other, then K=____

Because X and y are opposite numbers, then y = - X
By substituting the above formula, we can get 3x-2x = k5x-6x = - K
Because 3x-2x = - K, then x = - K is substituted into k5x-6x = - K
We can get - 5K & sup2; + 6K = - K
That is 5K & sup2; - 7K = 0
Then k = 0 or K = 7 / 5

5x + 2Y = 5 Y-Z = - 9 4Z + 3x = 13 find the value of X, y, Z

5x+2y=5 (1)
y-z=-9 (2)
4z+3x=13 (3)
From (1)
5x=5-2y x=1- (2/5)y
From (2) we get z = y + 9
Substituting x = 1 - (2 / 5) y, z = y + 9 into (3)
4(y+9)+3[1-(2/5)y]=13
It's time to tidy up
14y=-130
y=-65/7
x=1- (2/5)y=1-(2/5)(-65/7)=33/7
z=y+9=-65/7 +9=-2/7
x=33/7 y=-65/7 z=-2/7

X-2 + Z / 9 = 2x + y + 3Z / 10 = - (3x + 2y-4z) / (- 3) = 1

x-y+z=9 (1)
2x+y+3z=10 (2)
3x+2y-4z=3 (3)
(1)+(2)
3x+4z=19 (4)
(1)×2+(2)
5x-2z=21 (5)
(4)+(5)×2
13x=61
x=61/13
z=(19-3x)/4=16/13
y=x+z-9=-40/13