-x - y - 2z = 12 (equation 1) x - 3y = 15 (equation 2) x + 5y + 4z = -8 (equation 3) Rearrange equation 2: x = 3y + 15 Substitute equation 2 into equation 1: -(3y + 15) - y - 2z = 12 -4y - 2z = 27 -2z = 4y + 27 (multiply both sides by -2) 4z = -8y - 54 Substitute equation 2 into equation 3: (3y + 15) + 5y + 4z = -8 8y + 4z = - 23 4z = -8y - 23 Using the two new equations: 4z = 4z -8y - 54 = -8y - 23 -8y + 8y = -23 + 54 0 = 31 Since 0 can't equal to 31, no solution exists for these three equations.
Are you sure it is right? Would you knew Matrix? as this: -1 -1 -2 12 1 -3 0 15 1 5 4 -7 make r1*2+r3 , we have -1 3 0 16 1 -3 0 15 1 5 4 -8 then, if r1+r2, that's error, the reason in that it is wrong in 0=31. so, the equations mast error.
