Question

graph method 3x-2y+7=0
2x+3y-4=0​

Answer 1

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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 3x + 2y = 4 

3x + 2y = 4 

⇒2y = (4 – 3x) 

⇒y = (4-3x)/2 …(i) 

Putting x = 0,

we get y = 2 

Putting x = 2, we get y = -1 

Putting x = -2, we get y = 5 

Thus, we have the following table for the equation 3x + 2y = 4

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

Graph of 2x - 3y = 7 2x – 3y = 7 

⇒ 3y = (2x – 7) 

⇒ y = (2x-7)/3 …(ii) 

Putting x = 2,

we get y = -1 

Putting x = -1,

we get y = -3 

Putting x = 5, we get y = 1

Thus, we have the following table for the equation 2x – 3y = 7.

Now, plot the points P(-1, -3) and Q(5, 1).

The point C(2, -1) has already been plotted.

Join PB and QB and extend it on both ways.

Thus, line PQ is the graph of 2x – 3y = 7.

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

∴x = 2 and y = -1 are the solutions of the given system of equations.