Question

Solve for x and y:
$$\begin{gathered} 0.4x+0.3y=1.7 \\ 0.7x-0.2y=0.8 \end{gathered}$$

Answer 1

The given system of equations is
$$\begin{gathered} 0.4x+0.3y=1.7.....\left(i\right) \\ 0.7x-0.2y=0.8.....\left(ii\right) \end{gathered}$$
Multiplying (i) by 0.2 and (ii) by 0.3 and adding them, we get
$$\begin{gathered} 0.8x+2.1x=3.4+2.4 \\ \Rightarrow 2.9x=5.8 \\ \Rightarrow x=\frac{5.8}{2.9}=2 \end{gathered}$$
Now, substituting x = 2 in (i), we have
$$\begin{gathered} 0.4\times 2+0.3y=1.7 \\ \Rightarrow 0.3y=1.7-0.8 \\ \Rightarrow y=\frac{0.9}{0.3}=3 \end{gathered}$$
Hence, x = 2 and y = 3.