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, a_{1} = 1, b_{1} = 1, c_{1} = - 2;

And a_{2} = 2, b_{2} = - 1, c_{2} = - 1;

a_{1} /a_{2} = 1/2

b_{1} /b_{2} = - 1

c_{1} /c_{2} = 2

since a_{1}/a_{2} b_{1}/b_{2}

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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