Given:
[tex]\begin{gathered} 4a-5b=5\ldots\ldots\ldots(1) \\ 2a-3b=2\ldots\ldots\ldots(2) \end{gathered}[/tex]To solve for a and b:
Multiply equation (2) by 2 we get,
[tex]4a-6b=4\ldots\ldots\ldots(3)[/tex]Subtract equation (3) from (1) we get,
[tex]b=1[/tex]Substitute b=1 in equation (2) we get,
[tex]\begin{gathered} 2a-3(1)=2 \\ 2a=2+3 \\ 2a=5 \\ a=\frac{5}{2} \end{gathered}[/tex]Hence, the value of a and b are,
[tex]\begin{gathered} a=\frac{5}{2} \\ b=1 \end{gathered}[/tex]