4x+5y+z= 6?

Question

Solve by the addition method.
4x+5y+z= 6
2x-y+2z= 11
x+2y+2z= 6

Answer 1

I don't condone getting Homework answers here but I can help you. first you can eliminate 1 of the variables for example x by multiplying the 3rd eq. by -2 and adding eq. 2 and eq.3



2x-y+ 2z = 11 + (-2x - 4y - 4z = -12)

this will leave you with 0x -5y - 2z = -1



then you can do the same thing with eq. 1 and eq. 2

namely (4x + 5y + z = 6) +(-2)(2x-y+2z = 11)

this simplifies to



0x + 7y -3z = -16



you have to repeat the process and eventually you get a solution to 1 of the variable which you can then put back into one of the equations to find the other answers

Answer 2

Multiply the last row by -2 and add it to the second row; this gets rid of the x term



-2x-4y-4z=-12

+2x-1y+2z=+11



-5y-2z=-1



Then multiply the (original) third row by -4 and add it to the first row to eliminate x term again.



-4x-8y-8z=-24

+4x+5y+1z=+6



-3y-7z=-18

-5y-2z=-1 (from first part)



Now multiply the first of these by -5 and the second by 3 and add them to get rid of y term



+15y+35z=90

-15y- 6z=-3



29z=87



Divide by 29 to get z = 3

Plug this in to an equation with y and z only to get y, then plug both in to one of the original equations to get x. I hope you can do that part yourself.

Answer 3

X=2

Y=-1

Z=3



If you cant solve using the elimination method you can get your answer by fist solving it in a matrix. (on a graphing cal. to save time)