Answer: The required solution is (x, y) = (9, 5).
Step-by-step explanation: We are given to find the solution of the following system of linear equations :
[tex]2x+4y=38~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\10x+3y=105~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Multiplying equation (i) by 5, we have
[tex]5(2x+4y)=5\times38\\\\\Rightarrow 10x+20y=190~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Subtracting equation (ii) from equation (iii), we get
[tex](10x+20y)-(10x+3y)=190-105\\\\\Rightarrow 17y=85\\\\\Rightarrow y=\dfrac{85}{17}\\\\\Rightarrow y=5.[/tex]
Substituting the value of y in equation (i), we get
[tex]2x+4\times5=38\\\\\Rightarrow 2x+20=38\\\\\Rightarrow 2x=38-20\\\\\Rightarrow 2x=18\\\\\Rightarrow x=\dfrac{18}{2}\\\\\Rightarrow x=9.[/tex]
Thus, the required solution is (x, y) = (9, 5).
