Solve equation 0.2x+0.3y=1.3 0.4x+0.5y=2.3

0.2 x + 0.3 y = 1.3 ;  0.4 x + 0.5 y = 2.3
The given system of linear equations is:
0.2 x + 0.3 y = 1.3..............(1)
0.4 x + 0.5 y = 2.3...................(2)
From equation (1), 
0.3 y = 1.3 - 0.2 x
$\Rightarrow \quad y = \frac { 1.3 - 0.2 x } { 0.3 }$.........................(3)
Substituting this value of y in equation(2), we get
$0.4 x + 0.5 \left( \frac { 1.3 - 0.2 x } { 0.3 } \right) = 2.3$
$\Rightarrow$0.12 x + 0.65 - 0.1 x = 0.69
$\Rightarrow$0.12 x - 0.1 x = 0.69 - 0.65
$\Rightarrow$0.02 x = 0.04
$\Rightarrow$$\mathrm { x } = \frac { 0.04 } { 0.02 } = 2$
Substituting this value of x in equation(3), we get
$y = \frac { 1.3 - 0.2 ( 2 ) } { 0.3 } = \frac { 1.3 - 0.4 } { 0.3 } = \frac { 0.9 } { 0.3 } = 3$
Therefore, the solution is x = 2, y = 3, we find that both equation (1) and (2) are satisfied as shown below:
0.2 x + 0.3 y = ( 0.2 )( 2 )+( 0.3)( 3 ) = 0.4 + 0.9 = 1.3
0.4 x + 0.5 y= ( 0.4 )( 2 ) + ( 0.5 )( 3 ) } = 0.8 + 1.5 = 2.3
This verifies the solution.​​​​​​​

0.2x+0.3y = 1.3 ....... (i)
eq (i) ×10
2x+3y=13
0.4x+0.5y=2.3 ...... (ii)
eq(ii) ×10
4x+5y=23
from eq (i)
x =13-3y/2

putting value of x in eq (ii)
4(13-3y/2)+5y=23
26-6y+5y=23
26-y=23
y= 3
putting value of y in eq (i)
2x+3(3)=13
2x=13-9
x=4/2
x=2