Write four solutions for each of the following equations: <br/><br/>(i) $2 x+y=7$ <br/><br/>(ii) $\pi x+y=9$ <br/><br/>(iii) $x=4 y$

Solution:

(i) $2 x+y=7$

For $x=0$,

$2(0)+y=7$

$\Rightarrow y=7$

Therefore, $(0,7)$ is a solution of this equation.

For $x=1$,

$2(1)+y=7$

$\Rightarrow y=5$

Therefore, $(1,5)$ is a solution of this equation.

For $x=-1$

$2(-1)+y=7$

$\Rightarrow y=9$

Therefore, $(-1,9)$ is a solution of this equation.

For $x=2$,

$2(2)+y=7$

$\Rightarrow y=3$

Therefore, $(2,3)$ is a solution of this equation.

(ii) $\pi x+y=9$

For $x=0$,

$\pi(0)+y=9$

$\Rightarrow y=9$

Therefore, $(0,9)$ is a solution of this equation.

For $x=1$,

$\pi(1)+y=9$

$\Rightarrow y=9-\pi$

Therefore, $(1,9-\pi)$ is a solution of this equation.

For $x=2$,

$\pi(2)+y=9$

$\Rightarrow y=9-2 \pi$

Therefore, $(2,9-2 \pi)$ is a solution of this equation.

For $x=-1$,

$\pi(-1)+y=9$

$\Rightarrow y=9+\pi$

$\Rightarrow(-1,9+\pi)$ is a solution of this equation.

(iii) $x=4 y$

For $x=0$,

$0=4 y$

$\Rightarrow y=0$

Therefore, $(0,0)$ is a solution of this equation.

For $y=1$,

$x=4(1)=4$

Therefore, $(4,1)$ is a solution of this equation.

For $y=-1$

$x=4(-1)$

$\Rightarrow x=-4$

Therefore, $(-4,-1)$ is a solution of this equation.

For $x=2$,

$2=4 y$

$\Rightarrow y=\frac{2}{4}=\frac{1}{2}$

Therefore, $\left(2, \frac{1}{2}\right)$ is a solution of this equation.