Solve the following system of equations:

$0.4x\ +\ 0.3y\ =\ 1.7$
$0.7x\ –\ 0.2y\ =\ 0.8$

Given:

The given system of equations is:

$0.4x\ +\ 0.3y\ =\ 1.7$

$0.7x\ –\ 0.2y\ =\ 0.8$

To do:

We have to solve the given system of equations.

Solution:

The given system of equations can be written as,

$0.4x+0.3y=1.7$

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

$4x+3y=17$---(i)

$0.7x-0.2y=0.8$

$\Rightarrow 0.7x=0.2y+0.8$

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

$7x=2y+8$

$\Rightarrow x=\frac{2y+8}{7}$----(ii)

Substitute $x=\frac{2y+8}{7}$ in equation (i), we get,

$4(\frac{2y+8}{7})+3y=17$

$\frac{4(2y+8)}{7}+3y=17$ 

Multiplying by $7$ on both sides, we get,

$7(\frac{8y+32}{7})+7(3y)=7(17)$

$8y+32+21y=119$

$29y=119-32$

$29y=87$

$y=\frac{87}{29}$

$y=3$

Substituting the value of $y=3$ in equation (ii), we get,

$x=\frac{2(3)+8}{7}$

$x=\frac{14}{7}$

$x=2$

Therefore, the solution of the given system of equations is $x=2$ and $y=3$.

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Updated on: 10-Oct-2022

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