The normal equations are solved with rational elimination. The diagram is a solve certificate, so the displayed answer is recomputed from the displayed system.
highlighted = computed this step
Eliminate exactly
Gaussian elimination uses rational arithmetic, so no decimal approximation is needed.
[466141122]
The solution
The exact solution is a=11/10 and b=11/10. The diagram recomputes this from the displayed matrix.
a=11/10,b=11/10
Summary
The solve certificate is a trust boundary: change the displayed matrix or solution and validation rejects it.