Question

Solve the system of equations graphically:
2x + 3y = 4,
3x – y = -5

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
2x + 3y = 4  

⇒3y = (4 – 2x)
∴ y =` (4-2x)/3`             …(i)

Putting x = -1, we get y = 2.
Putting x = 2, we get y = 0.
Putting x = 5, we get y = -2.
Thus, we have the following table for the equation 2x + 3y = 4.

x	-1	2	5
y	2	0	-2

Now, plot the points A (-1, 2), B (2, 0) and C (5, -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 2x + 3y = 4.

3x – y = -5
⇒ y = (3x + 5) ……..(ii)
Putting x = -1, we get y = 2.
Putting x = 0, we get y = 5.
Putting x = -2, we get y = -1.
Thus, we have the following table for the equation 3x – y = -5.

x	-1	0	-2
y	2	5	-1

Now, plot the points P (0, 5) and Q (-2, -1). The point A (-1, 2) has already been plotted. Join PA and QA and extend it on both ways.
Thus, PQ is the graph of 3x - y = - 5.

The two graph lines intersect at A (-1. 2).
∴x = -1 and y = 2 are the solutions of the given system of equations.