Solve the following linear equation by …

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
{tex}\Rightarrow \quad y = \frac { 1.3 - 0.2 x } { 0.3 }{/tex}.........................(3)
Substituting this value of y in equation(2), we get
{tex}0.4 x + 0.5 \left( \frac { 1.3 - 0.2 x } { 0.3 } \right) = 2.3{/tex}
{tex}\Rightarrow{/tex}0.12 x + 0.65 - 0.1 x = 0.69
{tex}\Rightarrow{/tex}0.12 x - 0.1 x = 0.69 - 0.65
{tex}\Rightarrow{/tex}0.02 x = 0.04
{tex}\Rightarrow{/tex}{tex}\mathrm { x } = \frac { 0.04 } { 0.02 } = 2{/tex}
Substituting this value of x in equation(3), we get
{tex}y = \frac { 1.3 - 0.2 ( 2 ) } { 0.3 } = \frac { 1.3 - 0.4 } { 0.3 } = \frac { 0.9 } { 0.3 } = 3{/tex}
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.​​​​​​​