solve the equation graphically,2x+3y=2,x-2y=8
Answers
Answer:
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 2x + 3y = 2
2x + 3y = 2
⇒3y = (2 - 2x)
⇒3y = 2(1-x)
⇒y= 2(1-x) 3
...(i)
Putting x = 1, we get y = 0
Putting x = -2, we get y = 2
Putting x = 4, we get y = -2
Thus, we have the following table for the
equation 2x + 3y = 2
Thus, we have the following table for the
equation 2x + 3y = 2
Now, plot the points A(1, 0), B(-2, 2) and C(4, -2) on the graph paper.
Join AB and AC to get the graph line BC. Extend it on both ways.
Thus, the line BC is the graph of 2x + 3y = 2.
Graph of x - 2y = 8
x - 2y = 8
⇒ 2y = (x - 8)
X - - 8. ⇒y= ...(ii)
2 Putting x = 2, we get y = -3
Putting x = 4, we get y = -2
Putting x = 0, we get y = -4
Thus, we have the following table for the equation x - - 2y = 8.
Now, plot the points P(0, -4) and Q(2, -3). The point C(4, -2) has already been plotted. Join PQ and QC and extend it on both ways. Thus, line PC is the graph of x - 2y = 8.
The two graph lines intersect at C(4, -2). ..x = 4 and y = -2 are the solutions of the
given system of equations.