Combine the 2nd and 3rd equations. 3x will disappear:
2y + 5z = 7 This is true for any y and z, and is independent of x.
7-5z Solving for y, 2y = 7 - 5z, so that y = --------- 2
We have to eliminate x again by using the 1st and 2nd equations:
-2x - 6y - 2z = -2. We want the coeff. of x in the first eqn to be -3.
Therefore, mult. all terms of -2x - 6y - 2z = -2 by 3/2:
(3/2)(-2x - 6y - 2z = -2) = -3x -9y -3z =-3
Now add this version of the 1st row to the 2nd row:
-3x -9y -3z =-3 3x +2y +5z = 7 ---------------------- -7y + 2z = 4 7 - 5z We found earlier that y = ----------, and can elim. y by subst. this fraction into 2