Question

Solve the simultaneous equations $|x+2| +y=5$, $x-|y|=1$

Answer 1

(2, 1)

Answer 2

The deduction $x \ge 1$ from $x-|y|=1$ simplifies $|x+2|$ to $x+2$. Substituting $x=1+|y|$ into the first equation leads to $|x+2|+y=5 \implies (1+|y|)+2+y=5 \implies |y|+y=2$. For $y \ge 0$, this gives $2y=2 \implies y=1$. For $y < 0$, it yields $0=2$ (contradiction). Thus, $y=1$, and substituting back into $x=1+|y|$ gives $x=2$.