in this problem since we have x in the 3rd equatio. and -x in 2nd, we can add then2 equations together and cancel out the x
so to add equations i am going to add their left sides together and their right sides
left side:
-x +y +2z + (x +2y + 4z)
3y + 6z
right sides
3 + 0 = 3
now elimante x from another pairnof equations. i will do first and second. to get the x coefficient the same i will multiply second equation by 2.
2 * (-x + y + 2z) = 2 * 3
-2x + 2y + 4z = 6
add right sides and left sides
right sides
2x + 2y + z + (-2x + 2y + 4z)
4y + 5z
left sides
1 + 6 = 7
4y +5z = 7
so i have 3y + 6z = 3 and 4y + 5z = 7
i can multiply top by 4 and bottom by 3 to try ti cancel y
4 (3y + 6z) = 4 (3)
12y + 24z = 12
3 (4y + 5z) = 3 (7)
12y + 15z = 21
subtraxt this time since coefficients are both positive
left and right same time
12y + 24z - (12y + 15z) =12 - 21
9z = - 9
z = -1
solve for y from an easier equation
3y + 6z = 3
3y + 6 (-1) = 3
3y - 6 = 3
3y = 9
y = 3
now plug in and get x for any of the original equaltions
-x + y + 2z = 3
-x + (3) + 2 (-1) = 3
-x + 1 = 3
-x = 2
x = -2
