Question

Solve the system of equations graphically: 

3x + y + 1 = 0

2x - 3y + 8 = 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 3x + y + 1 = 0 

3x + y + 1 = 0 

⇒ y = (-3x - 1) …(i) 

Putting x = 0, we get y = -1. 

Putting x = -1, we get y = 2. 

Putting x = 1, we get y = -4. 

Thus, we have the following table for the equation 3x + y + 1 = 0.

x	0	-1	1
y	-1	2	-4

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

Join AB and AC to get the graph line BC. 

Extend it on both ways. 

Thus, BC is the graph of 3x + y + 1 = 0. 

Graph of 2x - 3y + 8 = 0 

2x - 3y + 8 = 0 

⇒ 3y = (2x + 8)

∴ y = \(\frac{2x+8}3\)

Putting x = -1, we get y = 2. 

Putting x = 2, we get y = 4. 

Putting x = -4, we get y = 0. 

Thus, we have the following table for the equation 2x - 3y + 8 = 0.

x	-1	2	-4
y	2	4	0

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

Join PB and BQ and extend it on both ways. 

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

The two graph lines intersect at B (-1. 2). 

∴x = -1 and y = 2