z-2a+b=0, a-2b+c=0, b-2c+d=0, c-2d+e=0, e-2f+g=0, f-2g+h=0, g-2h+i=0, h-2i+j=0, 86.4(d-e)+0.82(f-e)=0, 3.5(80-z)+86.4(a-z)+0.000000034(510^4-((z+460)^4))=0
You asked:
Solve the system of equations:\[\begin{aligned}z - 2 a + b &= 0\\a - 2 b + c &= 0\\b - 2 c + d &= 0\\c - 2 d + e &= 0\\e - 2 f + g &= 0\\f - 2 g + h &= 0\\g - 2 h + i &= 0\\h - 2 i + j &= 0\\86.4 \left(d - e\right) + 0.82 \left(f - e\right) &= 0\\3.5 \left(80 - z\right) + 86.4 \left(a - z\right) + 0.000000034 \left({510}^{4} - {\left( z + 460 \right)}^{4}\right) &= 0\end{aligned}\]