Question

Solve for x and y:
$$\begin{gathered} \frac{x}{2}-\frac{y}{9}=6 \\ \frac{x}{7}+\frac{y}{3}=5 \end{gathered}$$

−117 y=−1

Answer 1

The given system of equations can be written as
$$\begin{gathered} 9x-2y=108.....\left(i\right) \\ 3x+7y=105.....\left(ii\right) \end{gathered}$$
Multiplying (i) by 7 and (ii) by 2, we get
$$\begin{gathered} 63x+6x=108\times 7+105\times 2 \\ \Rightarrow 69x=966 \\ \Rightarrow x=\frac{966}{69}=14 \end{gathered}$$
Now, substituting x = 14 in (1), we have
$$\begin{gathered} 9\times 14-2y=108 \\ \Rightarrow 2y=126-108 \\ \Rightarrow y=\frac{18}{2}=9 \end{gathered}$$
Hence, x = 14 and y = 9.