Question

Solve the following pair of equations graphically.
$x+y=3;2x+5y=12$

Answer 1

Given, $x+y=3$
$\Rightarrow y=3-x$
when $x=0,y=3-0=3$
when $x=3,y=3-3=0$
when $x=2,y=3-2=1$
Thus, we have the following table:
$x=0,3,2$

$y=3,0,1$
Now plot the points $(0,3),(3,0)$ and $(2,1)$ on a graph paper. Join these points and extend the line on both sides to obtain the graph of $x+y=3.$
Again, $2x+5y=12\Rightarrow y=\frac{12-2x}{5}$
when $x=1,y=\frac{12-2\left(1\right)}{5}=2$
when $x=6,y=\frac{12-2\left(6\right)}{5}=0$
when $x=11,y=\frac{12-2\left(11\right)}{5}=-2$
Thus, we have the following table:
$x=1,6,11$

$y=2,0,-2$
Now, plot the points $(1,2),(6,0)$ and $(11,-2)$ on the same graph paper. Join these points and extend the line l2 on both sides to obtain the graph of $2x+5y=12.$
From the graph of the two equations, we see that line $l1$ and $l2$ intersect the coordinates of the point of intersection are $(1,2).$
Hence, we say that $x=1,y=2$ is the only solution of the given system of equations.