Question

Solve the system of equations graphically:
2x + 3y = 8,
x – 2y + 3 = 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 = 8
2x + 3y = 8
⇒3y = (8 – 2x)
⇒ `y=(8-2x)/3`    …(i)

Putting x = 1, we get y = 2.
Putting x = -5, we get y = 6.
Putting x = 7, we get y = -2.
Thus, we have the following table for the equation 2x + 3y = 8.

x	1	-5	7
y	2	6	-2

Now, plot the points A(1, 2), B(5, -6) and C(7, -2) 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 2x + 3y = 8.

Graph of x - 2y + 3 = 0
x – 2y + 3 = 0
⇒ 2y = (x + 3)
⇒ `y=(x+3)/2`    …(ii)

Putting x = 1, we get y = 2.
Putting x = 3, we get y = 3.
Putting x = -3, we get y = 0.
Thus, we have the following table for the equation x – 2y + 3 = 0.

x	1	3	-3
y	2	3	0

Now, plot the points P (3, 3) and Q (-3, 0). The point A (1, 2) has already been plotted. Join AP and QA and extend it on both ways.
Thus, PQ is the graph of x – 2y + 3 = 0.

The two graph lines intersect at A (1, 2).
∴ x = 1 and y = 2.