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

${\displaystyle \Rightarrow x=\frac{74-70y}{50}}$

Substituting ${\displaystyle x=\frac{74-70y}{50}}$ in equation (iv), we get

${\displaystyle 30\left(\frac{74-70y}{50}\right)+ 50y=50}$

${\displaystyle \Rightarrow \frac{3(74-70y)}{y}+50y=50}$

${\displaystyle \Rightarrow \frac{222-210}{5}+50y=50}$

${\displaystyle \Rightarrow 222-210y+250y=250}$

=> 40y = 250 - 222

=> 40y= 28

${\displaystyle \Rightarrow y=\frac{28}{40}=\frac{14}{20}=\frac{7}{10}=0.7}$

Putting y = 0.7 in x = ${\displaystyle \frac{74-70y}{50}}$ we get

${\displaystyle x=\frac{74-70\times 0.7}{50}}$

${\displaystyle =\frac{74-49}{50}}$

${\displaystyle =\frac{25}{50}}$

= 1/2 

= 0.5

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