Question

(x) 3a − 2b = −10; 2a + 3b = 2

Answer 1

$$\begin{gathered} 3a-2b=-10 \\ \Rightarrow a=\frac{-10+2b}{3}...\left(\mathrm{i}\right) \\ 2a+3b=2...\left(\mathrm{ii}\right) \\ \mathrm{Substituting}\left(\mathrm{i}\right)\mathrm{in}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{get}: \\ 2\times \left(\frac{-10+2b}{3}\right)+3b=2 \\ \Rightarrow -20+4b+9b=6 \\ \Rightarrow 13b=26 \\ \Rightarrow b=2 \\ \mathrm{Substituting}\text{b}=2\mathrm{in}\mathrm{eq}\left(\mathrm{i}\right),\mathrm{we}\mathrm{get}: \\ a=\frac{-10+2\times 2}{3} \\ \Rightarrow a=-2 \\ \mathrm{Hence},a=-2,b=2\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equations}. \end{gathered}$$