# What is the unique solution to this system of equation?

The solution sets:

-2x + 2y + 5z = -12 (A)

4x + 3y - Z = -8 (B)

-5x + 3y - 4z = 7 (C)

I aligned Set A with Set B, multiplying set B by 5 to cancel out the z's:

-2x + 2y + 5z = -12

20x + 15y -5z = -40

18x + 17y = -52 (D)

Next, I aligned Set B with Set C, multiplying Set B by 4 to cancel out the z's once more:

-16x - 12y + 4z = -32

-5x + 3y - 4z = 7

-21x - 9y = - 25 (E)

Aligning Sets D & E I multiplied D by 21 and E by 18 to cancel the x's:

378x + 357y = -1092

-378x - 162y = -450

195y = -1542/- 195

From this point I need assistance. Somewhere I believed I made a mistake but I do not know where.

• It should be $-16 x - 12 y + 4 z = 32$ not $-32$. Oct 24, 2021 at 2:08
• I got the solution as $x = -1, y = -2, z = -2$ Oct 24, 2021 at 2:15
• @HosamHajjir Peace and thank you. Did you multiply it by 4? Oct 24, 2021 at 2:22
• I multiplied by $(-4)$ Oct 24, 2021 at 2:26

Your last equation has only $$y$$ as a variable, so find its value. I can't read the formatting on the last line to say what the answer is. Then plug that $$y$$ into $$D$$ or $$E$$ and you find $$x$$. Now plug both $$x,y$$ into any of the first equations and you can find $$z$$.
When you aligned set B with set C you dropped a sign. You multiplied by $$-4$$, not $$4$$, so the right side should be $$32$$. A good way to find these is to follow the first paragraph to get a full solution. It will satisfy your last equation. Now plug it into each earlier equation and find where it fails. That is the place you made the error.