Question

draw the graph representing thw equations 2x = y + 2 amd 4x + 3y = 24 on the same graph paper.Find the area of triangle formed by these lines and the X axis​

Answer 1

Step-by-step explanation:

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.