Question

solve the equation graphically,2x+3y=2,x-2y=8​

Answer 1

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

Thus, we have the following table for the

equation 2x + 3y = 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)

X - - 8. ⇒y= ...(ii)

2 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.

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.

The two graph lines intersect at C(4, -2). ..x = 4 and y = -2 are the solutions of the

given system of equations.