Find the value of $k$, if $x = 2$, $y = 1$ is a solution of the equation $2x + 3y = k$.

From the choices given below, choose the equation whose graphs are given in Fig. $(i)$ and Fig. $(ii)$.

For Fig. $(i)$                                            For Fig. $(ii)$

$(a)$ $y=x$                                              $(a)$ $y=x+2$

$(b)$ $x+y=0$                                     $(b)$ $y=x-2$

$(c)$ $y=2 x$                                           $(c)$ $y=-x+2$

$(d)$ $2+3 y=7 x$                                $(d)$ $x+2 y=6$

Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case : $-2 x+3 y=6$

For each of the graphs given in Fig. select the equation whose graph it is from the choices given below :

$(a)$ For Fig. $(i)$,

$(i)$ $x+y=0$           $(ii)$ $y=2 x$            $(iii)$ $y=x$             $(iv)$ $y=2 x+1$

$(b)$ For Fig. $(ii)$,

$(i)$ $x+y=0$           $(ii)$ $y=2 x$            $(iii)$ $y=2x+4$             $(iv)$ $y=x-4$

$(c)$ For Fig. $(iii)$,

$(i)$ $x+y=0$           $(ii)$ $y=2 x$            $(iii)$ $y=2x+1$             $(iv)$ $y=2 x-4$

Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case : $2 x=-\,5 y$

Check the solutions of the equation $x -2y = 4$ and which are not : $(\sqrt{2},\, 4 \sqrt{2})$