Question

Solve the system of equations graphically:

2x + 3y = 2,

x – 2y = 8

Solve graphically: 2x + 3y = 2, x – 2y = 8

Answer 1

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 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.

The two graph lines intersect at C(4, –2).

∴ x = 4 and y = –2 are the solutions of the given system of equations.

Answer 2

Given,

2x + 3y = 2

⇒ `y = (2 - 2x)/3`

x	1	4	–2
y	0	–2	2

And x – 2y = 8

⇒ `y = (x - 8)/2`

x	0	8	4
y	–4	0	–2

Plotting the above points and drawing the lines joining them, we get the graph of above equations.

Two obtained lines intersect at point P(4, –2).

Hence, Solution of the given equation is x = 4, y = –2.