Question

Solve the following system of equations graphically:
$x+2y=5,2x-3y=-4.$
Also, find the points, where these lines meet the x-axis.

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 x + 2y = 5

x + 2y = 5
⇒ 2y = (5 − x)
∴ $y=\frac{5-x}{2}$ ...........(i)
Putting x = 1, we get y = 2.
Putting x = 3, we get y = 1.
Putting x = 5, we get y = 0.
Thus, we have the following table for the equation x + 2y = 5.

x	1	3	5
y	2	1	0

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

Graph of 2x − 3y = −4
2x − 3y = −4
⇒ 3y = (2x + 4)
∴ $y=\frac{2x+4}{3}$............(ii)
Putting x = 1, we get y = 2.
Putting x = −2, we get y = 0.
Putting x = 4, we get y = 4.
Thus, we have the following table for the equation 2x − 3y = −4.

x	1	−2	4
y	2	0	4

Now, plot the points P(4, 4) and Q(−2, 0). The point A(1, 2) has already been plotted. Join PA and QA to get the graph line PQ. Extend it on both ways.
Then, PQ is the graph of the equation 2x − 3y = −4.

The two graph lines intersect at A(1, 2).
∴ The solution of the given system of equations x = 1 and y = 2.
Hence, the lines (i) and (ii) intersect x-axis at Q(−2, 0) and C(5, 0), respectively.