Solve the system of equations x3y2z10 2x4y3z1 4x2y5z9 Give a

Solve the system of equations

x+3y-2z=-10

-2x+4y-3z=1

4x-2y+5z=9

Give answers in form {x,y,z}. Please show all steps.

x + 3y-2z=-10

-2x + 4y -3z=1

4x-2y+5z=9

Multiplying first equation by 2 and add it to second equation,we get

2x + 6y - 4z -2x + 4y -3z= -20+1

10y - 7z=-19

multiplying first by -4 and add it to the last,we get

-4x -12y +8z + 4x-2y+5z= 49

-14y+13z=49

Now we have two equations

10y-7z=-19

-14y +13z=49

multiplying first by 7 and second by 5 and add them,we get

70y -49z-70y + 65z= -133 + 245

16z= 112

z= 7

-14y+13(7)=49

-14y= -42

y=3

x + 3(3)-2(7)=-10

x=-5

solution is {-5,3,7}