In my first step of solving this three step equation i eliminated both my x and z what do I do next

Question

X+y-2z=8

5x-3y+z=-6

-2x-y+4z=-13

 

2(x+y-2=8)

-2x-y+4z=-13

 

2x+2y-4z=8

-2x-y+4z=-13

Answer 1

x+y-2z=8

5x-3y+z=-6

-2x-y+4z=-13

multiply first equation by 2 on both sides !!!

2x+2y-4z=16, now with last equation...

-2x-y+4z=-13

add

y=3 (work with first two equations)

x+3-2z=8

x-2z=5

5x-9+z=-6

5x+z=3 (multiply this equation by 2)

x-2z=5

10x+2z=6 (add this and the one above)

11x=11

x=1

1+3-2z=8 (first equation)

4-2z=8

-2z=4

z=-2

x=1, y=3, z=-2

 

 

 

 

Answer 2

Hi Tasha,

 

You are on the right track. I only see one mistake so far in your steps. When you multiply the first equation by 2, make sure to multiply all terms by two, including the 8 on the right side of the equation. So now you have:

 

2x + 2y - 4z = 16

-2x - y  +4z = -13

 

So we can add the two equations and eliminate the x and z terms to get:

 

2y - y = 16 - 13

y = 3

 

Now we need to do a similar elimination with two other sets of equations, but this time look to eliminate only the x or z terms. Let's look at the 1st and 2nd equation:

 

 x + 2y - 2z = 8

5x - 3y + z = -6

 

Multiply the second equation by two so that we can eliminate the z terms:

 

     x + y - 2z = 8

2(5x - 3y + z = -6)

 

 

   x +  y  - 2z = 8

10x - 6y + 2z = -12

 

So eliminate the z terms and you are left with:

 

x + 10x + 2y - 6y = -4

11x -5y = -4

 

We already solved for y, so we plug in that value (y=3) and solve for x:

 

11x - 5(3) = -4

11x - 15 = -4

11x = 11

x = 1

 

Now we know x and y, so plug back into any of the three equations and solve for z.