Answer:
(x=6,y=5,z=9)
Step-by-step explanation:
The given system is
x+y+z=20 ------>(1)
13x+0y+6z=132 ------->(2)
150x+90y+139z=2601------>(3)
Make y the subject in the first equation to get: [tex]y=20-x-z-------(4)[/tex]
Put equation (4) in equation (3) to get:
150x+90(20-x-z)+139z=2601
150x+180-90x-90z+139z=2601
60x+49z=801---->(5)
We solve equation (2) and (5) simultaneously
13x+6z=132 ------->(2)
60x+49z=801---->(5)
Make x the subject in equation (2) to get:
[tex]x=\frac{132-6z}{13}[/tex]
Put it in (5)
[tex]60(\frac{132-6z}{13})z+49z=2601[/tex]
[tex]\frac{277z+7920}{13}=801[/tex]
[tex]277z+7920=10413[/tex]
[tex]277z=2493[/tex]
[tex]z=9[/tex]
[tex]x=\frac{132-6*9}{13}=6[/tex]
From 6+y+9=20
y=20-15=5
