Solve the following system of equations:\(\frac{x}{2}\) + y = 0.8; 7/

1.	Solve the following system of equations:\(\frac{x}{2}\) + y = 0.8; 7/(x+ \(\frac{y}{2}\)) = 10
Answer» The given pair of equations are: \(\frac{x}{2}\) + y = 0.8 ⇒ x + 2y = 1.6…… (a) 7/(x + \(\frac{ y}{2}\)) = 10 ⇒7 = 10(x +\(\frac{ y}{2}\)) ⇒7 = 10x + 5y Let’s, multiply LHS and RHS of equation (a) by 10 for easy calculation So, we finally get 10x + 20y = 16 .........(i) And, 10x + 5y = 7 ……(ii) Now, subtracting two equations we get, ⇒ (i) – (ii) 15y = 9 ⇒ y = \(\frac{3}{5}\) Next, putting the value of y in the equation (i) we get, x = [16 − 20(3/5)]/10 ⇒ \(\frac{(16 – 12)}{10}\) = \(\frac{4}{10}\) ∴ x = \(\frac{2}{5}\) Thus, the value of x and y obtained are \(\frac{2}{5}\) and \(\frac{3}{5}\) respectively.

Solve the following system of equations:\(\frac{x}{2}\) + y = 0.8; 7/(x+ \(\frac{y}{2}\)) = 10

Answer»

The given pair of equations are:

\(\frac{x}{2}\) + y = 0.8

⇒ x + 2y = 1.6…… (a)

7/(x + \(\frac{ y}{2}\)) = 10

⇒7 = 10(x +\(\frac{ y}{2}\))

⇒7 = 10x + 5y

Let’s, multiply LHS and RHS of equation (a) by 10 for easy calculation

So, we finally get

10x + 20y = 16 .........(i)

And, 10x + 5y = 7 ……(ii)

Now, subtracting two equations we get,

⇒ (i) – (ii)

15y = 9

⇒ y = \(\frac{3}{5}\)

Next, putting the value of y in the equation (i) we get,

x = [16 − 20(3/5)]/10

⇒ \(\frac{(16 – 12)}{10}\) = \(\frac{4}{10}\)

∴ x = \(\frac{2}{5}\)

Thus, the value of x and y obtained are \(\frac{2}{5}\) and \(\frac{3}{5}\) respectively.