1. ## System of equations

2. Start by getting rid of fractions:
42a - 7b + 7c = 61
and
21a - 21b - 14c = 43

3. yea i did that already and ive gotten so many diffrent answers. and even plugged ihem back in to see if they r right... but no luck... but here is my last work. i found z and y which was z-25/91 and y=160/819 is that right?

basically i tried to ways. one was making 1x+2y-2z=3 into everything equal to 1. and another i did was i just did a regular system of quation.. but yeah. help please.!

4. Well, I'm not typing out the steps; but here's the solution:
x = 143/91, b = 0, c = -65/91

5. hi
$\left\{\begin{matrix}
x+2y-2z=3\\
6x-y+z=\frac{61}{7}\\
3x-3y-2z=\frac{43}{7}
\end{matrix}\right.$

your solution is $[x=\frac{11}{7},y=0,z=-\frac{5}{7}]$

6. (1): x + 2y - 2z = 3
(2): $2x - \frac{1}{3}y + \frac{1}{3}z = \frac{61}{21}$
(3): $\frac{3}{2}x - \frac{3}{2}y - z = \frac{43}{14}$

(1) x 42 $\rightarrow$ 42x + 84y - 84z = 126
(2) x 21 $\rightarrow$ 42x - 7y + 7z = 61
(3) x 28 $\rightarrow$ 42x - 42y - 28z = 86

(2) - (3) $\rightarrow$ 35y + 35z = -25
7y + yz = -5
7z = -5 - 7y ...(4)

From (1) $\rightarrow$ 42x = 126 - 84y + 84z
(4) into (1) $\rightarrow$ 42x = 126 - 84y + 12(-5 - 7y)
42x = 126 - 60 - 84y - 84y
42x = 66 - 168y ...(5)

(4) and (5) into (2) $\rightarrow$ (66 - 168y) - 7y + (-5 - 7y) = 61
182y = 0
y = 0 ...(6)

(6) into (4) $\rightarrow$ 7z = -5 - 0
$z = -\frac{5}{7}$ ...(7)

(6) and (7) into (1) $\rightarrow$ $x + 0 - 2(-\frac{5}{7}) = 3$
x = $3 - \frac{10}{7}$
x = $\frac{11}{7}$

7. Originally Posted by ukorov
(1): x + 2y - 2z = 3
(2): $2x - \frac{1}{3}y + \frac{1}{3}z = \frac{61}{21}$

(1) x 42 $\rightarrow$ 42x + 84y - 84z = 126
(2) x 21 $\rightarrow$ 42x - 7y + 7z = 61
Much easier to leave (1) as is, and multiply (2) by 6:

(1): x + 2y - 2z = 3
(2):12x -2y+ 2z = 122/7
13x = 3 + 122/7
x = 11/7

8. oh wth!? i actually did get that 11/7 and the zero but i got the 11/7 for z for some reason. and i also got the zero for the y, but i got both of those answers during diffrent tries of doing this problem.... but thxs everyone for the help!

9. Originally Posted by Wilmer
Much easier to leave (1) as is, and multiply (2) by 6:

(1): x + 2y - 2z = 3
(2):12x -2y+ 2z = 122/7
13x = 3 + 122/7
x = 11/7
probably~ but I usually leave this "improvement" work to the question asker