Question

Find the solution of $x+2y=10$ and $2x+4y=8$ graphically.

Answer 1

Given, $x+2y=10$

$\Rightarrow x=10-2y$

For $y=3$

$x=10-2\left(3\right)=4$

For $y=4$
$x=10-2\left(4\right)=2$

$x$	$4$	$2$
$y$	$3$	$4$

For $2x+4y=8$

$\Rightarrow x+2y=4$

$\Rightarrow x=4-2y$

For $y=1$

$x=4-2\left(2\right)=2$

For $y=3$

$x=4-2\left(3\right)=-2$

$x$	$2$	$-2$
$y$	$1$	$3$

The graph $x+2y=10$ cuts the $x$ and $y$-axis at $(10,0)$ and $(0,5)$ respectively, while the graph of $2x+4y=8$ cuts the $x$ and $y$-axis at $(4,0)$ and $(0,2)$ respectively.

Since the graph consists of a pair of parallel lines, the system of equations has no solution.