​ Find the solution set of the system of equations: 4/x + 5y = 7 and 3/x + 4y = 5. ​

Question

Find the solution set of the system of equations:  \(\frac{4}{X}\) + 5y = 7 and \(\frac{3}{X}\) + 4y = 5.

Answer 1

Let \(\frac{1}{X}\) = a. Then the system of equations become

4a + 5y = 7.........(i)

3a + 4y = 5............(ii)

Multiplying equation (1) by 3 and equation (2) by 4 and subtracting equation (2) from equation (1), we get

\(\Rightarrow\) Putting y = –1 in (1), we get

4a – 5 = 7 \(\Rightarrow\) 4a = 12 \(\Rightarrow\) a = 3 \(\Rightarrow\) x = \(\frac{1}{3}\)

\(\therefore\) The solution set is \(\big(\frac{1}{3},-1\big)\).