Solve the following system of equations:4/x + 5y = 7; 3/x + 4y = 5

1.	Solve the following system of equations:4/x + 5y = 7; 3/x + 4y = 5
Answer» Taking 1/x = u, the given equation becomes 4u + 5y = 7………(i) 3u + 4y = 5………(ii) Subtracting (ii) from (i), we get 4u + 5y – (3u + 4y) = 7 – 5 ⇒ u + y = 2 ⇒ u = 2 – y………(iii) Using (iii) in (i), 4(2 – y) + 5y = 7 ⇒ 8 – 4y + 5y = 7 ⇒ y = -1 Putting y = -1 in (iii), we find u u = 2 – (-1) ⇒ u = 3 ⇒ x = 1/u = \(\frac{1}{3}\) Hence, the solution for the given system of equations is x = \(\frac{1}{3}\) and y = -1

Answer»

Taking 1/x = u, the given equation becomes

4u + 5y = 7………(i)

3u + 4y = 5………(ii)

Subtracting (ii) from (i), we get

4u + 5y – (3u + 4y) = 7 – 5

⇒ u + y = 2

⇒ u = 2 – y………(iii)

Using (iii) in (i),

4(2 – y) + 5y = 7

⇒ 8 – 4y + 5y = 7

⇒ y = -1

Putting y = -1 in (iii), we find u

u = 2 – (-1)

⇒ u = 3

⇒ x = 1/u = \(\frac{1}{3}\)

Hence, the solution for the given system of equations is x = \(\frac{1}{3}\) and y = -1

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