Solve the following pair of linear equations?

$3x+4y=10$ and $2x-2y=2$

 For what value of $k$ the following system of equations have unique solutions

$2x+ky=1; 3x-5y=7$

Solve for $x$ and $y$:

$$\begin{gathered} \frac{5}{x-1}+\frac{1}{y-2}=2 \\ \frac{6}{x-1}-\frac{3}{y-2}=1 \end{gathered}$$

For what values of $a$ and $b$ does the following pair of linear equations have an infinite number of solutions.

$2x+3y=7; a(x+y)-b(x-y)=3a+b-2$