91Ó°ÊÓ

Here system of two equations $$\begin{gathered} \left\{3x-8y=20 \\ x+3y=1\right\} \end{gathered}$$ are given.

We need to find the solution to these equations.

Here both equations are in standard form,

$$\begin{gathered} 3\mathrm{x}-8\mathrm{y}=20\left(1\right) \\ \mathrm{x}+3\mathrm{y}=1\left(2\right) \\ \mathrm{To}\mathrm{eliminate}\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{multiply}\left(2\right)×3 \\ 3\mathrm{x}+9\mathrm{y}=3\left(3\right) \\ \mathrm{Now}\mathrm{the}\mathrm{term}\mathrm{of}\mathrm{x}\mathrm{equal}\mathrm{in}\mathrm{equation}\left(1\right)\&\left(3\right),\mathrm{when}\mathrm{we}\mathrm{substract}\left(1\right)\&\left(3\right)\mathrm{we}\mathrm{get} \\ -17\mathrm{y}=17 \\ \mathrm{y}=\frac{-17}{17} \\ \mathrm{y}=-1, \\ \mathrm{Substitute}\mathrm{this}\mathrm{y}=-1\mathrm{in}\left(1\right)\mathrm{or}\left(2\right)\mathrm{we}\mathrm{get}\mathrm{value}\mathrm{for}\mathrm{x} \\ \mathrm{So},\mathrm{substitue}\mathrm{y}=-1\mathrm{in}\left(2\right) \\ \mathrm{x}+3×-1=1 \\ \mathrm{x}=1+3 \\ \mathrm{x}=4 \\ \mathrm{S}o(4,-1)\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{for}\mathrm{system}\mathrm{of}\mathrm{equations}. \end{gathered}$$

When we substitute solution (4,-1) in the given system equations and if both sides are equal in the given equations then (4,-1) is the original solution. Hence

$$\begin{gathered} 3\mathrm{x}-8\mathrm{y}=20,\mathrm{put}\mathrm{x}=4,\mathrm{y}=-1\mathrm{in}\mathrm{this}\mathrm{orginal}\mathrm{equation}\mathrm{we}\mathrm{get} \\ 3×4-8×-1=20 \\ 12+8=20 \\ 20=20,\mathrm{both}\mathrm{sides}\mathrm{are}\mathrm{equal} \\ \mathrm{Now},\mathrm{x}+3\mathrm{y}=1 \\ S\mathrm{ubstitue}\mathrm{the}\mathrm{values}\mathrm{x}=4\mathrm{and}\mathrm{y}=-1\mathrm{then} \\ 4-3=1 \\ 1=1,\mathrm{both}\mathrm{sides}\mathrm{are}\mathrm{equal} \\ \mathrm{So}\mathrm{ordered}\mathrm{pair}(4,-1)\mathrm{is}\mathrm{a}\mathrm{solution}\mathrm{for}\mathrm{given}\mathrm{equations}. \end{gathered}$$

$$\begin{gathered} 3x-8y=20,putx=4,y=-1inthisorginalequationweget \\ 3×4-8×-1=20 \\ 12+8=20 \\ 20=20,bothsidesareequal \\ x+3y=1.substituethevaluesx=4andy=-1then \\ 4-3=1 \\ 1=1bothsidesareequal \\ Soorderedpair(4,-1)isasolutionforgivenequations \end{gathered}$$