Question

1. Find whether the following equations are consistent, if so, solve them.
(a) x + y + 2z = 4; 2x-y + 3z = 9; 3x-y - z = 2 [1, -1, 2]

Answer 1

Answer:

first you take two pairs of equations and eliminate one of the variables 

multiply third equation by 2 and add to first equation 2x+4y-2z+x+y+2z=10+11 ... 3x+5y=21 ... z is eliminated 

multiply third equation by 3 and add to first equation 3x+6y-3z+x+y+3z=15+14 ... 4x+7y=29 ... z is eliminated 

next, you take the pair of new equations and eliminate one of the variables 

multiply first new equation by 4 and second new equation by -3 and add 12x+20y-12x-21y=84-87 ... -y=-3 ... y=3 

take this value to one of the new equations to find x ... 3x+5(3)=21 ... x=2 

take values of y and x to an original equation to find z ... 2+3+2z=11 ... z=3