Write four solutions for equations : $2x + y = 7$
When $x=0$, $2(0)+y=7$ $\Rightarrow 0+y=7$
$\Rightarrow $ $y=7$ $\therefore$ Solution is $(0,\,7)$.
When $x=1$, $2(1)+y=7$ $\Rightarrow y=7-2$
$\Rightarrow $ $y=5$ $\therefore$ Solution is $(1,\,5)$.
When $x=2$, $2(2)+y=7$ $\Rightarrow y=7-4$
$\Rightarrow $ $y=3$ $\therefore$ Solution is $(2,\,3)$.
When $x=3$, $2(3)+y=7$ $\Rightarrow y=7-6$
$\Rightarrow $ $y=1$ $\therefore$ Solution is $(3,\,1)$.
Solve the equation $2x + 1 = x -3$, and represent the solution(s) on
$(i)$ the number line,
$(ii)$ the Cartesian plane.
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case : $2 x=-\,5 y$
Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a$, $b$ and $c$ in each case : $-2 x+3 y=6$
The taxi fare in a city is as follows :
For the first kilometre, the fare is Rs. $8$ and for the subsequent distance it is Rs. $5$ per $km$. Taking the distance covered as $x\, km$ and total fare as Rs. $y$, write a linear equation for this information, and draw its graph.
Give the geometric representations of $y = 3$ as an equation
$(i)$ in one variable
$(ii)$ in two variables