Solve graphically the system of equations3x-2y=4and 2x-3y=7
Answers
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
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