Question

3x -y=5 and x+2y=4 solve graphically​

Answer 1

Answer

x+2y=4 …(i)

2y=4−x

y=(4−x)/2

When x=0,y=(4−0)/2=4/2=2

When x=2,y=(4−2)/2=2/2=1

When x=4,y=(4−4)/2=0/2=0

x= 0 ,2 ,4

y= 2 ,1 ,0

Mark the above points on graph. Join them.

3x−2y=4 ..(ii)

2y=3x−4

y=(3x−4)/2

When x=0,y=(3×0−4)/2=(0−4)/2=−4/2=−2

When x=2,y=(3×2−4)/2=(6−4)/2=2/2=1

When x=4,y=(3×4−4)/2=(12−4)/2=8/2=4

Mark the above points on graph. Join them.

x= 0 ,2 ,4

y= −2 ,1 ,4

It is clear from the graph that the two lines intersect at (2,1).

So the solution of the given equations are x=2 and y=1.

The area of the triangle formed by these lines and Xaxis=1/2×base×height

=1/2×2.7×1

=1.35sq. units

Hence area of the triangle is 1.35sq.unite