Answer:
The solution of the system of equations is
x=2,y=7,z=8
Step-by-step explanation:
we have
3x-2y+z=0
isolate the variable z
z=2y-3x ------> equation A
4x+y-3z=-9 ----> equation B
9x-2y+2z=20 ----> equation C
substitute equation A in equation B and equation C
4x+y-3(2y-3x)=-9
4x+y-6y+9x=-9
13x-5y=-9 -------> equation D
9x-2y+2(2y-3x)=20
9x-2y+4y-6x=20
3x+2y=20 ----> equation E
Solve the system
13x-5y=-9 -------> equation D
3x+2y=20 ----> equation E
Multiply equation E by 2.5 both sides
2.5*(3x+2y)=20*2.5
7.5x+5y=50 -----> equation F
Adds equation D and equation F
13x-5y=-9
7.5x+5y=50
------------------
13x+7.5x=-9+50
20.5x=41
x=41/20.5
x=2
<u><em>Find the value of y</em></u>
substitute the value of x in the equation E
3(2)+2y=20
6+2y=20
2y=20-6
2y=14
y=7
<u><em>Find the value of z</em></u>
Substitute the value of x and the value of y in equation A
z=2y-3x
z=2(7)-3(2)
z=14-6
z=8
therefore
The solution of the system of equations is
x=2,y=7,z=8
