Solve the following system of equations:
$0.5x\ +\ 0.7y\ =\ 0.74$
$0.3x\ +\ 0.5y\ =\ 0.5$

Given:

The given system of equations is:

$0.5x\ +\ 0.7y\ =\ 0.74$

$0.3x\ +\ 0.5y\ =\ 0.5$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

$0.5x+0.7y=0.74$

Multiplying by $100$ on both sides, we get,

$50x+70y=74$---(i)

$0.3x+0.5y=0.5$

$\Rightarrow 0.3x=0.5-0.5y$

Multiplying by $10$ on both sides, we get,

$3x=5-5y$

$\Rightarrow x=\frac{5-5y}{3}$----(ii)

Substitute $x=\frac{5-5y}{3}$ in equation (i), we get,

$50(\frac{5-5y}{3})+70y=74$

$\frac{50(5-5y)}{3}+70y=74$ 

Multiplying by $3$ on both sides, we get,

$3(\frac{250-250y}{3})+3(70y)=3(74)$

$250-250y+210y=222$

$-40y=222-250$

$-40y=-28$

$y=\frac{28}{40}$

$y=\frac{7}{10}$

Substituting the value of $y=\frac{7}{10}$ in equation (i), we get,

$50x+70(\frac{7}{10})=74$

$50x=74-49$

$50x=25$

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

$x=\frac{1}{2}$

Therefore, the solution of the given system of equations is $x=\frac{1}{2}$ and $y=\frac{7}{10}$. 

Tutorialspoint

Updated on: 10-Oct-2022

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