Okay, so I\'ve been working this stupid problem for 2 days nowand cannot get an

Question

Okay, so I've been working this stupid problem for 2 days nowand cannot get an answer that checks. 2x+4y+6z=2 x=2z 2x+3y-z=-5 I know I have to substitute 2z for x in the first and thirdequation. 4z+4y+6z=2 4z+3y-z=-5 Combine like terms 10z+4y=2 3z+3y=-5 So, at this point, I am eliminating the y variable by comingup with an LCM and multipling the respective equations. 3(10z+4y=2) -4(3z+3y=-5) Which leaves 30z+12y=6 -12z-12y=20 Then adding the two equations together 18z=26 Dividing by 18 on both sides z=13/9 So if x=2z, then x=26/9 right? Here's where I'm getting all jacked up. Plugging back inand solving for y. 2(26/9)+3y-13/9=-5 52/9+3y-13/9=-5 39/9+3y=-5 3y=-5-39/9 3y=2/3 y=2/9 So x=26/9 y=2/9 and z=13/9 Here's the check: 2(26/9)+4(2/9)+6(13/9)=2 52/9+8/9+79/9=2 139/9=2 15 4/9 really really doesn't equal 2. So as you can see, I've done my work but it appears I'mmissing something, something really simple I'm sure. Anytakers? Okay, so I've been working this stupid problem for 2 days nowand cannot get an answer that checks. 2x+4y+6z=2 x=2z 2x+3y-z=-5 I know I have to substitute 2z for x in the first and thirdequation. 4z+4y+6z=2 4z+3y-z=-5 Combine like terms 10z+4y=2 3z+3y=-5 So, at this point, I am eliminating the y variable by comingup with an LCM and multipling the respective equations. 3(10z+4y=2) -4(3z+3y=-5) Which leaves 30z+12y=6 -12z-12y=20 Then adding the two equations together 18z=26 Dividing by 18 on both sides z=13/9 So if x=2z, then x=26/9 right? Here's where I'm getting all jacked up. Plugging back inand solving for y. 2(26/9)+3y-13/9=-5 52/9+3y-13/9=-5 39/9+3y=-5 3y=-5-39/9 3y=2/3 y=2/9 So x=26/9 y=2/9 and z=13/9 Here's the check: 2(26/9)+4(2/9)+6(13/9)=2 52/9+8/9+79/9=2 139/9=2 15 4/9 really really doesn't equal 2. So as you can see, I've done my work but it appears I'mmissing something, something really simple I'm sure. Anytakers?

Explanation / Answer

You did a mistake in calculating y as 3y=-5-(39/9)=-84/9 so y= - 84/27        = -28/9

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