1.

Solve the following system of equations:x + 2y = 3/2; 2x + y = 3/2

Answer»

The given pair of equations are: 

x + 2y = \(\frac{3}{2}\) …………(i) 

2x + y = \(\frac{3}{2}\)………….(ii) 

Let us eliminate y from the given equations. The coefficients of y in the given equations are 2 and 1 respectively. The L.C.M of 2 and 1 is 2. So, we make the coefficient of y equal to 2 in the two equations.

Multiplying equation (i) x 1 and (ii) x 2 

⇒ x + 2y = \(\frac{3}{2}\) ……………(iii) 

4x + 2y = 3 ………………. (iv) 

Subtracting equation (iii) from (iv) 

(4x – x) + (2y - 2y) = 3x = 3 – (\(\frac{3}{2}\)) 

⇒ 3x = \(\frac{3}{2}\) 

⇒ x = \(\frac{1}{2}\)

Putting x = \(\frac{1}{2}\) in equation (iv) 

4(\(\frac{1}{2}\)) + 2y = 3 

⇒ 2 + 2y = 3 

∴ y= \(\frac{1}{2}\)

The solution of the system of equation is x = \(\frac{1}{2}\) and y = \(\frac{1}{2}\).


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