##### Write an equation of a line passing through the point representing solution of the pair of linear equations x + y = 2 and 2x-y = 1 How many such lines can we find?

Given pair of linear equations is

x + y-2 = 0 …(i)

and 2x-y-1 = 0 …(ii)

On comparing with ax + by + c = 0

Here, a1 = 1, b1 = 1, c1 = - 2;

And a2 = 2, b2 = - 1, c2 = - 1;

a1 /a2 = 1/2

b1 /b2 = - 1

c1 /c2 = 2

since a1/a2 b1/b2

So, both lines intersect at a point. Therefore, the pair of equations has a unique solution. Hence, these equations are consistent.

Now, x + y = 2 or y = 2-x

If x = 0 then y = 2 and if x = 2 then y = 0

 x 0 2 y 2 0 Points A B

and

If x = 0 then y = - 1 if x = then y = 0 and if x = 1 then y = 1

 x 0 1/2 1 y - 1 0 1 Points C D E

Plotting the points A (2,0) and B(0,2), we get the straight line AB. Plotting the points C(0,- 1) and D(1/2, 0), we get the straight line CD.

The lines AB and CD intersect at E (1, 1).

Hence, infinite lines can pass through the intersection point of linear equations and i.e. E (1, 1) like as y = x, x + 2y = 3, x + y = 2 and so on.

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