The solution of  $6x-5y-16=0$,  $7x-13y+10=0$

Given : Two equations

$6x-5y-16=0$      ------ 1

$7x-13y+10=0$   ------ 2

From  - 1

$6x-5y=16$

$-5y=16-6x$

$5y=6x-16$

$y=\frac{6x-16}{5}$

Substitute this value in equation – 2

2         $\Rightarrow$    $7x-13\left(\frac{6x-16}{5}\right)+10=0$

Multiply with $\text{'}5\text{'}$

$35x-13(6x-16)+50=0$

$35x-78x+208+50=0$

$-43x+258=0$

$-43x=-258$

$x=\frac{258}{43}$

$x=6$

Substitute $x=6$ in

equation 1

$\Rightarrow$   $6\left(6\right)-5y-16=0$

$36-5y-16=0$

$-5y-20=0$

$20=5y$

$\frac{20}{5}=y$

$4=y$

$y=4$

$\therefore$ The solution is  $(6,4)$