Question

solve the following:

x+1/4 - y+21/3 = -1
1-x/5 + 3-y/4 =13/20

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{equations}\mathrm{are}: \\ \frac{\mathrm{x}+1}{4}-\frac{\mathrm{y}+21}{3}=-1 \\ \Rightarrow 3\mathrm{x}-4\mathrm{y}=69....\left(1\right) \\ \frac{1-\mathrm{x}}{5}+\frac{3-\mathrm{y}}{4}=\frac{13}{20} \\ \Rightarrow 4\mathrm{x}+5\mathrm{y}=6....\left(2\right) \\ \mathrm{Multipli}\left(1\right)\mathrm{by}5\mathrm{and}\left(2\right)\mathrm{by}4,\mathrm{we}\mathrm{get} \\ 15\mathrm{x}-20\mathrm{y}=345....\left(3\right) \\ 16\mathrm{x}+20\mathrm{y}=24.....\left(4\right) \\ \mathrm{Adding}\left(3\right)\mathrm{and}\left(4\right),\mathrm{we}\mathrm{get} \\ 31\mathrm{x}=369 \\ \Rightarrow \mathrm{x}=\frac{369}{31} \\ \mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get} \\ 4\times \frac{369}{31}+5\mathrm{y}=6 \\ \Rightarrow 5\mathrm{y}=6-\frac{1476}{31} \\ \Rightarrow 5\mathrm{y}=-\frac{1290}{31} \\ \Rightarrow \mathrm{y}=-\frac{258}{31} \end{gathered}$$