Find (x, y, z)

[nycmathguy]

 

[MathLover1]

x-y=4.........eq.1
4x+y=-9........eq.2
xz+yz=60........eq.3
--------------------------------
x-y=4.........eq.1, solve for x
x=4+y........eq.1a

4x+y=-9........eq.2, solve for x
x=-9/4-y/4........eq.2a

from eq.1a and eq.2a we have

4+y=-9/4-y/4.......... solve for y
y/4+y=-9/4-4
5y/4=-9/4-16/4
5y/4=-25/4
5y=-25
y=-5

go to
x-y=4.........eq.1, substitute y
x-(-5)=4
x+5=4
x=4 -5
x=-1

go to

xz+yz=60........eq.3, substitute y and x
-1*z-5z=60
-6z=60
z=60/-6
z=-10

so, x=-1, y=-5, z=-10

then find
(x+y+z)/-2 =(-1-5-10)/-2
(x+y+z)/-2 =(-16)/-2
(x+y+z)/-2 =8

 

[nycmathguy]

x-y=4.........eq.1
4x+y=-9........eq.2
xz+yz=60........eq.3
--------------------------------
x-y=4.........eq.1, solve for x
x=4+y........eq.1a

4x+y=-9........eq.2, solve for x
x=-9/4-y/4........eq.2a

from eq.1a and eq.2a we have

4+y=-9/4-y/4.......... solve for y
y/4+y=-9/4-4
5y/4=-9/4-16/4
5y/4=-25/4
5y=-25
y=-5

go to
x-y=4.........eq.1, substitute y
x-(-5)=4
x+5=4
x=4 -5
x=-1

go to

xz+yz=60........eq.3, substitute y and x
-1*z-5z=60
-6z=60
z=60/-6
z=-10

so, x=-1, y=-5, z=-10

then find
(x+y+z)/-2 =(-1-5-10)/-2
(x+y+z)/-2 =(-16)/-2
(x+y+z)/-2 =8

I need more practice with 3 equations in 3 unknowns.