When \(y=x\) and \(x+y=10\) are graphed in the standard \((x,y)\) coordinate plane, at what point do they intersect?

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Use substitution.

$$ y=x $$ $$ x+y = 10 $$ $$ x+x = 10 $$ $$ 2x=10 $$ $$ x=5 $$ $$ y= 5 $$