Question

Find the solution to the system of equations.

x-4y-2z=1
x+5y+2z=-1
y+3z=10

What about an equation where you have nothing to plug in?

Answer 1

x-4y-2z=1
x+5y+2z=-1
y+3z=10

(1)--->
y=10-3z

eliminate 2 equation
x-4y-2z=1
x+5y+2z=-1
eliminate x by minus then all follow......
(x-x) + (-4y-5y) + (-2z-2z)= 1-(-1)
0+(-9y) + (-4z) =2
-9y-4z=2
subtitute y with (1) equation
-9(10-3z) - 4z =2
-90+27z-4z=2
-90+23z=2
23z=92
z=4

find y,,
y=10-3z
=10-3(4)
=-2

find x by subtitute z and y...choose any equation above..
x-4y-2z=1
x-4(-2)-2(4)=1
x+8-8=1
x=1

.:hence::.x=1,,y=-2,,z=4
prove all by subtitute z,x and y into any equation....
x+5y+2z=-1
(1)+5(-2)+2(4)=-1
1-10+8=-1
-1=-1

proven!!!