.
Eliminate
{6X-2y =11
{-9X+3y=16
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6x - 2y = 11 (1)
-9x + 3y = 16 (2)
Multiply equation (1) by 3 and equation (2) by 2. Then add.
In this way you eliminate y and obtain a single equation for x:
18x - 18x = 3*11 - 2*16,
0x = 1.
The last equation has no solution.
Hence, the original system has no solution, too.
This system is inconsistent.
You may discover it from the very beginning, just before I started these transformations.
Indeed, left sides of the original equations are proportional.
But the right sides are not proportional with the same coefficient of proportionality.
It just indicates that the system is inconsisted.
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