Explain the question given above,
and how is this graph formed?
Class 10th, rd sharma, pair of linear equations in two variables.
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Solution:
Given,
x + y = 3……. (i)
2x + 5y = 12……. (ii)
For equation (i),
When y = 0, we have x =3
When x= 0, we have y =3
Thus, we have the following table giving points on the line x + y = 3
For equation (ii),
We solve for y:
⇒ y = (12 – 2x)/5
So, when x = 1
y = (12 – 2(1))/5 = 2
And, when x = 6
⇒ y = (12 – 2(6))/5 = 0
Thus, we have the following table giving points on line 2x + 5y = 12
Graph of the equations (i) and (ii) is as below:
Clearly, the two lines intersect at a single point P (1, 2).
Hence, x= 1 and y = 2