Question

2x+y-19=0 on the same axes, draw the graphs of the following equation​

Answer 1

Answer:

stion 1:

2x+3y=2,x-2y=8.

ANSWER:

On a graph paper, draw a horizontal line X'OX and a vertical line YOY' representing the x-axis and y-axis, respectively.

Graph of 2x + 3y = 2

2x + 3y = 2

⇒ 3y = (2 − 2x)

⇒ 3y = 2(1 − x)

⇒ y =

2(1-x)

3

...(i)

Putting x = 1, we get y = 0

Putting x = − 2, we get y = 2

Putting x = 4, we get y = −2

Thus, we have the following table for the equation 2x + 3y = 2.

x 1 −2 4

y 0 2 −2

Now, plot the points A(1, 0), B(− 2 , 2) and C(4, − 2) on the graph paper.

Join AB and AC to get the graph line BC. Extend it on both ways.

Thus, the line BC is the graph of 2x + 3y = 2.

Graph of x − 2y = 8

x − 2y = 8

⇒ 2y = ( x − 8)

⇒ y=

x-8

2

...(ii)

Putting x = 2, we get y = −3

Putting x = 4, we get y = −2

Putting x = 0, we get y = −4

Thus, we have the following table for the equation x - 2y = 8.

x 2 4 0

y − 3 − 2 − 4

Now, plot the points P(0, − 4) and Q(2, − 3). The point C(4, −2) has already been plotted. Join PQ and QC and extend it on both ways.

Thus, line PC is the graph of x − 2y = 8.