The given system of equations is:
[tex]2x=5(2-y);y=3(-x+5)[/tex]Simplify to get:
[tex]\begin{gathered} 2x=10-5y \\ 2x+5y=10\ldots(i) \\ y=-3x+15 \\ 3x+y=15\ldots(ii) \end{gathered}[/tex]Multiply (ii) by 5 to get:
[tex]15x+5y=75\ldots(iii)[/tex]Subtract (i) from (iii) to get:
[tex]\begin{gathered} 15x+5y=75 \\ -2x-5y=-10 \\ 13x=65 \\ x=\frac{65}{13}=5 \end{gathered}[/tex]Substitute x=5 in (ii) to get:
[tex]\begin{gathered} 3(5)+y=15 \\ y=0 \end{gathered}[/tex]Solution set {5,0}.
