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for equation y=x
y=1 then x=1 (1,1)
y= 4 then x=4 (4,4)
for equation y= -x
y=-3 then x=3(3,-3)
y=4 then x=-4(-4,4)
We observe that lines of equation y=x and y=-x intersect at point (0,0).
Hence this pair of equation is consistent and has only on solution
and :x=-y I.e 1,-1;3,-3;4,-4