Question

Solve the following pair of linear equations graphically : x + 3y = 6, 2x - 3y = 12. Also shade the region bounded by the line 2x - 3y = 12 and both the co-ordinate axes.

Answer 1

In this question, we have been given a pair of equations that is x + 3y = 6 and 2x + 3y = 12 and we have been asked to find the solution of the equations. To solve this question, we will first find the couple of points for both the equation by hit and trial. So, we get,

For equation x + 3y = 6

At x = 0

0 + 3y = 6

y = 2

At y = 0,

x + 3(0) = 6

x = 6

At y = 1,

x + 3(1) = 6

x = 3

So, we can say, for x + 3y = 6, we get,

x	6	3	0
y	0	1	2

Or we can say (6, 0), (3, 1), (0, 2) are the points which satisfy x + 3y = 6

Similarly, we will find the points for the equation 2x + 3y = 122. We will get,

At x = 0,

2(0) + 3y = 12

y = 4

At y = 0,

2(x) + 3(0) = 12

x = 6

At y = 2,

2x + 3(2) = 12

x = 3

So, we can say, for 2x + 3y = 122, we get,

x	6	3	0
y	0	2	4

Or we can say (6, 0), (3, 2), (0, 4) are the points which satisfy 2x + 3y = 122

Now, we will use these points to plot on the graph and represent the pair of equations. So, we get,

Now, we can see that the pair of lines meet each other at (6, 0). So, we can say that (6, 0) is the answer of x + 3y = 6 and 2x + 3y = 12.

Answer 2

Plotting the above points and drawing lines joining them, we get the graphs of the equations x + 3y = 6 and 2x - 3y = 12

.

Answer 3

x + 3y = 6 or y = \(\frac{6-X}{3}\) .........(i)

x	3	6	0
y	1	0	2

2x - 3y = 12 ...........(ii)

or,  y = \(\frac{2X-12}{3}\)

x	0	6	3
y	-4	0	-2

Plotting the above points and drawing lines joining them, we get the graphs of the equations x + 3y = 6 and 2x - 3y = 12

The two lines intersect each other at point B (6,0).

Hence, x = 6 and y = 0

Again \(\triangle\)OAB is the region bounded by the line 2x - 3y = 12 and both the co-ordinate axis.