Question

solve the equations:

1) 4x +2y =17

7x - 2y = 8

2) 3x - 7y +10 =0

y - 2x -3 = 0

Answer 1

$$\begin{gathered} \left(1\right).\mathrm{The}\mathrm{given}\mathrm{equations}\mathrm{are}: \\ 4x+2y=17...........\left(1\right) \\ \mathrm{and}7x-2y=8............\left(2\right) \\ \mathrm{Adding}\left(1\right)\mathrm{and}\left(2\right)\mathrm{we}\mathrm{get} \\ 11x=25 \\ \Rightarrow x=\frac{25}{11} \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get}, \\ 7\times \frac{25}{11}-2y=8 \\ \Rightarrow \frac{175}{11}-2y=8 \\ \Rightarrow -2y=8-\frac{175}{11} \\ \Rightarrow -2y=\frac{88-175}{11} \\ \Rightarrow -2y=-\frac{87}{11} \\ \Rightarrow y=\frac{87}{11\times 2} \\ \Rightarrow y=\frac{87}{22} \end{gathered}$$
$\mathrm{Hence},x=\frac{25}{11}\mathrm{and}y=\frac{87}{22}$


$$\begin{gathered} \left(2\right).\mathrm{The}\mathrm{given}\mathrm{equations}\mathrm{are}: \\ 3x-7y+10=0 \\ y-2x-3=0 \\ \mathrm{The}\mathrm{given}\mathrm{equations}\mathrm{can}\mathrm{be}\mathrm{written}\mathrm{as}: \\ 3x-7y=-10..........\left(1\right) \\ y-2x=3...........\left(2\right) \\ \mathrm{From}\mathrm{equation}\left(2\right)\mathrm{we}\mathrm{get}, \\ y=2x+3.............\left(3\right) \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}y\mathrm{from}\left(3\right)\mathrm{in}\left(1\right) \\ 3x-7\left(2x+3\right)=-10 \\ \Rightarrow 3x-14x-21=-10 \\ \Rightarrow -11x-21=-10 \\ \Rightarrow -11x=-10+21 \\ \Rightarrow -11x=11 \\ \Rightarrow x=-1 \\ \mathrm{Putting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\left(3\right),\mathrm{we}\mathrm{get}, \\ y=2\times \left(-1\right)+3 \\ \Rightarrow y=-2+3 \\ \Rightarrow y=1 \\ \mathrm{Hence},x=-1\mathrm{and}y=1 \end{gathered}$$