Question

ya الما حالا =1 ه ماه - 5 ما- : - امت 6) x - 6y + 4 = -12 x + y - 47 = 12 2x + 2 + 57 = -15 =

Answer 1

In order to solve this system by elimination, let's first isolate the variable x in the first equation and use its value in the other equations:

$\begin{gathered} x-y-2z=-6 \\ x=y+2z-6 \\ \\ 3x+2y=-25 \\ 3(y+2z-6)+2y=-25 \\ 3y+6z-18+2y=-25 \\ 5y+6z=-7\text{ (equation 1)} \\ \\ -4(y+2z-6)+y-z=12 \\ -4y-8z+24+y-z=12 \\ -3y-9z=-12\text{ (equation 2)} \end{gathered}$

Now, isolating y in the equation 2 and using it in the equation 1:

$\begin{gathered} -3y=9z-12 \\ y=4-3z \\ \\ 5(4-3z)+6z=-7 \\ 20-15z+6z=-7 \\ -9z=-27 \\ z=3 \\ \\ y=4-3\cdot3 \\ y=4-9 \\ y=-5 \\ \\ x=y+2z-6 \\ x=-5+2\cdot3-6 \\ x=-5 \end{gathered}$

So the solution for the system is x = -5, y = -5 and z = 3.