Answer :
Given the system of equations:
[tex]\begin{gathered} 2x+4y=7.8\rightarrow(1) \\ 9x-5y=0.6\rightarrow(2) \end{gathered}[/tex]We will solve the system using the substitution method.
Solve the equation (1) for (x):
[tex]\begin{gathered} 2x=-4y+7.8\rightarrow(\div2) \\ x=-2y+3.9\rightarrow(3) \end{gathered}[/tex]Substitute with (x) from equation (3) into equation (2)
[tex]9(-2y+3.9)-5y=0.6[/tex]Solve the equation to find (y)
[tex]\begin{gathered} 9\cdot(-2y)+9\cdot3.9-5y=0.6 \\ -18y+35.1-5y=0.6 \\ -18y-5y=0.6-35.1 \\ -23y=-34.5 \\ y=\frac{-34.5}{-23}=1.5 \end{gathered}[/tex]Substitute with (y) into equation (3) to find (x)
[tex]\begin{gathered} x=-2\cdot1.5+3.9 \\ x=-3+3.9 \\ x=0.9 \end{gathered}[/tex]So, the answer will be:
[tex](x,y)=(0.9,1.5)[/tex]