Question

2x-5y=4 and 2x+y=8 by graphical method​

Answer 1

Step-by-step explanation:

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

Graph of 2x - 5y + 4 = 0

2x – 5y + 4 = 0

⇒5y = (2x + 4)

⇒

$y= \frac{2x + 4}{5} …(i)$

Putting x = -2, we get y = 0.

Putting x = 3, we get y = 2.

Putting x = 8, we get y = 4.

Thus, we have the following table for the equation 2x - 5y + 4 = 0.

x -2 3 8

y 0 2 4

Now, plot the points A (-2, 0), B (3, 2) and C(8, 4) on the graph paper.

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

Thus, AC is the graph of 2x - 5y + 4 = 0.

Graph of 2x + y - 8 = 0

2x + y - 8 = 0

⇒ y = (8 – 2x) …(ii)

Putting x = 1, we get y = 6.

Putting x = 3, we get y = 2.

Putting x = 2, we get y = 4.

Thus, we have the following table for the equation 2x + y - 8 = 0.

x 1 3 2

y 6 2 4

Now, plot the points P (1, 6) and Q (2, 4). The point B (3, 2) has already been plotted. Join PQ and QB and extend it on both ways.

Thus, PB is the graph of 2x + y - 8 = 0.

Refer attachment

The two graph lines intersect at B (3, 2).

∴x = 3 and y = 2