Question

3x+y+z=14
-x+2y-3z=-9
5x-y+5z=30
linear equations solve by elimination

Answer 1

looks like the y's would be the first line of attack

add 1st and last ----> 8x + 6z = 44
4x + 3z = 22

double the first ---> 6x + 2y + 2z = 28
keep second as is --> -x + 2y - 3z = -9
subtract them:
7x + 5z = 37

4x + 3z = 22 --times 5 --> 20x + 15z = 110
7x + 5z = 37 --times 3 --> 21x + 15z = 111
subtract the last two
x = 1

sub into 7x+5z=37
7+5z = 37
5z = 30
z = 6

back into the 1st:
3 + y + 6 = 14
y = 5

x=1 , y=5 , z=6

Answer 2

so in elimination you always add first, then subtract the for the next equation?
thank you, Aaron