Question

Draw the graph of the pair of linear equations
2x + y = 4 and 2x - y = 4
Write the vertices of triangle formed by these lines and y axis also find the area of this triangle

Answer 1

Answer:

Explanation:

Equations given 1.)2x+y=4

2.)2x-y=4

Now we have to draw a graph using these equations.

So let's find the values of x and y used for making a graph.

First equation,2x+y=4

X|0|2

Y|4|0

And, second equation,2x-y=4

X|0|2

Y|-4|0

Then after making the graph as shown the figure comes out be a triangle as said in the question.

So, area of a triangle=1/2×b×h

We got b=8 and h=2

Hence,area=1/2×8×2

Which is equal to 8sq.units

Answer 2

Answer:

2x+y=4...(i)

⇒y=4−2x

If x=0,y=4−2(0)=4−0=4

x=1,y=4−2(1)=4−2=2

x=2,y=4−2(2)=4−4=0

x 0 1 2 3

y 4 2 0 −2

(i) A B C −2

2x−y=4...(ii)

⇒y=2x−4

If x=0,y=2(0)−4=0−4=−4

x=1,y=2(1)−4=2−4=−2

x=2,y=2(2)−4=4−4=0

x 0 1 2 3 4

y −4 −2 0 2 4

(ii) E F G H I

triangle formed by the lines with y -axis ΔAEC coordinates of vertices are A(0,4),E(0,−4) and C(2,0)

Area of ΔAEC=

2

1

Base×Altitude

=

2

1

AE×CO

=

2

1

×[4−(−4)]×(2−0)

=

2

1

×8×2=8

∴ Area of ΔAEC= Square units.