Question

solve the system of three equations
2x-3y+5z=13
-3x+3y-2z=-8
5x-2y+4z=2

solve with full steps and work thank you and for every variable using eather substitution method or elimination

Answer 1

The system of three equations
2x-3y+5z=13 equation 1
-3x+3y-2z=-8 equation 2
5x-2y+4z=2 equation 3

we'll use elimintaion method as well as substitution
add the first two equation y will get get cancelled
2x-3y+5z+-3x+3y-2z=13-8
we get -x+3z=5 let this be equation 4


from second equation we have
3y=3x+2z-8
y=(3x+2z-8)/3
substituting this in equation 3
5x-2(3x+2z-8)/3+4z=2
15x-6x-4z+16+12z=6
9x+8z=-10 let this be equation 5
from equation 4 we have x=3z-5
put this in equation 5
27z-45+8z=-10
35z=35
z=1
now x=3z-5
x=3*1-5
x=-2
we had found earlier
y=(3x+2z-8)/3
x=-2 and z=1
y=(3*-2+2*1-8)/3
y=(-6+2-8)/3
y=-12/3
y=-4
so x=-2 y=-4 and z=1