Question

Solve the following systems of equations:

$$\begin{gathered} 3x-\frac{y+7}{11}+2=10 \\ 2y+\frac{x+11}{7}=10 \end{gathered}$$

Answer 1

The given equations are:

$$\begin{gathered} 3x-\frac{y+7}{11}+2=10 \\ \Rightarrow 3x-\frac{\left(y+7\right)}{11}=8 \\ \Rightarrow \frac{33x-y-7}{11}=8 \\ \Rightarrow 33x-y-7=88 \\ \Rightarrow 33x-y=95........\left(1\right) \end{gathered}$$

$$\begin{gathered} 2y+\frac{x+11}{7}=10 \\ \Rightarrow \frac{14y+x+11}{7}=10 \\ \Rightarrow 14y+x+11=70 \\ \Rightarrow 14y+x=59 \\ \Rightarrow x+14y=59.........\left(2\right) \end{gathered}$$

Multiply equation (1) by , we get

$462x-14y=1330......\left(3\right)$

adding (2) and (3), we get

$$\begin{gathered} \left(x+14y\right)+\left(462x-14y\right)=59+1330 \\ \Rightarrow 463x=1389 \\ \Rightarrow x=3 \end{gathered}$$

$$\begin{gathered} \mathrm{Substituting}\mathrm{the}\mathrm{value}\mathrm{of}x\mathrm{in}\left(2\right),\mathrm{we}\mathrm{get} \\ 3+14y=59 \\ \Rightarrow 14y=59-3 \\ \Rightarrow 14y=56 \\ \Rightarrow y=4 \end{gathered}$$

Hence the value of x and y are and