Question

Solve the following system of equations $2x-y=1$ and $x+2y=8$ graphically. Also, write the co-ordinate of the point where these lines intersect the y-axis.

Answer 1

The given equations are
$2x-y=1$
and $x+2y=8$
From equation (i)
$2x-y=1$
$\Rightarrow y=2x-1$
when $x=0,y=2\times 0-1=-1$
when $x=1,y=2\times 1-1=1$
when $x=2,y=2\times 2-1=3$
Table for equation (i)
$x=0,1,2$

$y=-1,1,3$
Similarly from equation (ii), we get
$2y=8-x\Rightarrow y=\frac{8-x}{2}$
when $x=2,y=\frac{8-2}{2}=\frac{6}{2}=3$
when $x=0,y=\frac{8-0}{2}=4$
when $x=4,y=\frac{8-4}{2}=\frac{4}{2}=2$
Table for equation (ii)
$x=2,0,4$

$y=3,4,2$
Now plotting and joining the points from the table (i) and (ii) on the same graph paper. We find that their points of intersection are $(2,3).$
Hence the required solution is $(2,3).$ The above lines are intersecting y-axis at $(0,-1)$ and $(0,4)$ respectively.