Question 7
Let $x,y,z$ be three positive real numbers such that $$x+|y|+\{z\}=13.2,\qquad |x|+\{y\}+z=14.3,\qquad \{x\}+y+|z|=15.1.$$ Here $[a]$ denotes the greatest integer $\le a$ and $\{b\}$ denotes the fractional part of $b$ (for example, $[5.4]=5$ and $\{4.3\}=0.3$). Find $x$.
Source notation conflict: the equations print absolute-value bars, but the accompanying definition uses floor brackets. Retain both as printed. For manual assessment, explain whether the literal system is consistent and, separately, what follows if the bars were intended as floor brackets.
Source notation conflict: the equations print absolute-value bars, but the accompanying definition uses floor brackets. Retain both as printed. For manual assessment, explain whether the literal system is consistent and, separately, what follows if the bars were intended as floor brackets.