Question

Find a, if the line 3x +at =8 passes through the intersection of lines represented by equations 3x-2y=10 and 5x+y =8

Answer 1

$$\begin{gathered} 3\mathrm{x}-2\mathrm{y}=10...\left(1\right) \\ 5\mathrm{x}+\mathrm{y}=8...\left(2\right) \\ \mathrm{From}\mathrm{eqn}\left(1\right),\mathrm{we}\mathrm{get} \\ 3\mathrm{x}=10+2\mathrm{y} \\ \mathrm{x}=\frac{10+2\mathrm{y}}{3} \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{x}\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get} \\ 5\left(\frac{10+2\mathrm{y}}{3}\right)+\mathrm{y}=8 \\ \frac{50+10\mathrm{y}+3\mathrm{y}}{3}=24 \\ 50+13\mathrm{y}=72 \\ 13\mathrm{y}=22 \\ \mathrm{y}=\frac{22}{13} \\ \mathrm{so}, \\ \mathrm{x}=\frac{10+2\left({\displaystyle \frac{22}{13}}\right)}{3}=\frac{130+44}{39}=\frac{174}{39}=\frac{58}{13} \\ \mathrm{As},3\mathrm{x}+\mathrm{ay}=8\mathrm{passes}\mathrm{through}\mathrm{point}\mathrm{of}\mathrm{intersection}\left(\frac{58}{13},\frac{22}{13}\right) \\ 3\left(\frac{58}{13}\right)+\mathrm{a}\left(\frac{22}{13}\right)=8 \\ \frac{174+22\mathrm{a}}{13}=8 \\ 174+22\mathrm{a}=104 \\ 22\mathrm{a}=-70 \\ \mathrm{a}=-\frac{70}{22}=-\frac{35}{11}\mathrm{ANS}... \end{gathered}$$