Question

Solve the system of equations graphically:

x + 2y + 2 = 0, 3x + 2y – 2 = 0

Solve the following system of equations graphically:

x + 2y + 2 = 0, 3x + 2y – 2 = 0

Answer 1

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 + 3y = 4

x + 2y + 2 = 0

⇒ 2y = (–2 – x)

∴ `y = (-2 - x)/2`   ...(i)

Putting x = –2, we get y = 0.

Putting x = 0, we get y = –1.

Putting x = 2, we get y = –2.

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

x	–2	0	2
y	0	–1	–2

Now, plot the points A(–2, 0), B(0, –1) and C(2, –2) 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 x + 2y + 2 = 0.

Graph of 3x + 2y – 2 = 0

3x + 2y – 2 = 0

⇒ 2y = (2 – 3x)

∴ `y = (2 - 3x)/2`   ...(ii)

Putting x = 0, we get y = 1.

Putting x = 2, we get y = –2.

Putting x = 4, we get y = –5.

Thus, we have the following table for the equation 3x + 2y – 2 = 0.

x	0	2	4
y	1	–2	–5

Now, plot the points P(0, 1) and Q(4, –5). The point C(2, –2) has already been plotted.

Join PC and QC and extend it on both ways.

Thus, PQ is the graph of 3x + 2y – 2 = 0.

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

∴ x = 2 and y = –2.