Question

Write an equation with variables on both sides that has no solution. Explain why it has no solution.

Answer 1

$\displaystyle \sf Let:\\\\ I) \ -(-3x+2)=4x-x+3 \\\\ 3x-2=3x+3 \\\\ -2\neq 3 \rightarrow \varnothing \\\\ II) \\x^2+7x+16=0 \\\\ D=49-64=-15 \ ; \ D<0 \rightarrow \varnothing \\\\\\ III) - \left \{ {{x+y=3} \ \ |\cdot2 \atop {2y+2x=2}} \right.=> 2x+2y-2x-2y=6-2 \\\\ . \qquad \qquad \qquad \qquad \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0 \neq 4 \ \rightarrow \varnothing$