Question

Solve the following simultaneous equations by substitution method.
(i) 2x + 3y = $-$ 4; x $-$ 5y = 11

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)2x+3y=-4...\left(1\right) \\ x-5y=11 \\ \Rightarrow x=11+5y...\left(2\right) \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\mathrm{eq}\left(1\right),\text{we get:} \\ 2\left(11+5y\right)+3y=-4 \\ \Rightarrow 22+10y+3y=-4 \\ \Rightarrow 22+13y=-4 \\ \Rightarrow 13y=-26 \\ \Rightarrow y=\frac{-26}{13} \\ \Rightarrow y=-2 \\ \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}y\mathrm{in}\mathrm{eq}\left(2\right),\text{we get:} \\ x=11+\left(5\times -2\right) \\ \Rightarrow x=1 \\ \therefore x=1\mathrm{and}y=-2\mathrm{is}\mathrm{the}\mathrm{solution}. \end{gathered}$$