Question

Solve for $xandy$

$\frac{x+2y+1}{2x-y+1}=2;\frac{3x-y+1}{x-y+3}=5$

Answer 1

Step 1 : Simplification of equation by cross multiplication method

$$\begin{gathered} \frac{x+2y+1}{2x-y+1}=2 \\ \Rightarrow x+2y+1=2(2x-y+1) \\ \Rightarrow x+2y+1=4x-2y+2 \\ \Rightarrow 4x-2y+2-x-2y-1=0 \\ \Rightarrow 3x-4y+1=0 \\ \Rightarrow 3x-4y=-1...................................\left(1\right) \\ Wehave, \\ \frac{3x-y+1}{x-y+3}=5 \\ \Rightarrow 3x-y+1=5(x-y+3) \\ \Rightarrow 3x-y+1=5x-5y+15 \\ \Rightarrow 5x-5y+15-3x+y-1=0 \\ \Rightarrow 2x-4y+14=0 \\ \Rightarrow 2x-4y=-14................................\left(2\right) \end{gathered}$$

Step 2 : Solving (1) and (2) using elimination method

$$\begin{gathered} equation\left(1\right)-\left(2\right)\Rightarrow x=13 \\ putx=13inequation\left(2\right) \\ equation\left(2\right)\Rightarrow 26-4y=-14 \\ \Rightarrow 26+14=4y \\ \Rightarrow 4y=40 \\ \Rightarrow y=10 \end{gathered}$$

Therefore the values of $x=13andy=10$