Question

Solve the following systems of equations:

0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5

Answer 1

The given systems of equations is

0.5x + 0.7y = 0.74   .....(i)

0.3x + 0.5y = 0.5  ....(ii)

Multiplying (i) and (ii) by 100, we get

50x + 70y = 74  .....(iii)

30x + 50y = 50 ....(iv)

From (iii), we get

50x = 74 - 70y

`=> x = (74 - 70y)/50`

Substituting `x = (74 - 70y)/50 ` in equation (iv), we get

`30((74 - 70y)/50) +  50y = 50`

`=> (3(74 - 70y))/y + 50y = 50`

`=> (222 - 210)/5 + 50y = 50`

`=> 222 - 210y + 250y = 250`

=> 40y = 250 - 222

=> 40y= 28

`=> y = 28/40 = 14/20 = 7/10 = 0.7`

Putting y = 0.7 in x = `(74 - 70y)/50` we get

`x = (74 - 70 xx 0.7)/50`

`= (74 - 49)/50`

`= 25/50`

= 1/2 

= 0.5

Hence, solution of the given system of equation is x = 0.5, y = 0.7