Answer:
no solution
Step-by-step explanation:
–5x – 12y – 43z = –136
–4x – 14y – 52z = –146
21x + 72y + 267z = 756
Every coefficient of the second equation is a multiple of 2, so divide both sides by 2.
Every coefficient of the third equation is a multiple of 3, so divide both sides by 3.
–5x – 12y – 43z = –136
–2x – 7y – 26z = –73
7x + 24y + 89z = 252
Let's call the above system the "simplified original system."
Using the simplified original system, multiply the first equation by -2 and the second equation by 5. Then add them.
10x + 24y + 86z = 272
(+) -10x - 35x - 130z = 365
------------------------------------------
-11y - 44z = 637
Now we have an equation with only y and z.
Now, using the simplified original system, multiply the second equation by 7 and the third equation by 2. Then add them.
–14x – 49y – 182z = –511
(+) 14x + 48y + 178z = 504
-------------------------------------------
-y - 4z = -7
Now we have a system in 2 unknowns, y and z.
-11y - 44z = 637
-y - 4z = -7
Multiply the second equation by -11 and add to the first equation.
-11y - 44z = 637
(+) 11y + 44z = 77
-----------------------------
0 = 714
Since 0 = 714 is false, this system has no solution.
