Question

the point of intersection of the lines x+y-1=0, x-y-1=0 is​

Answer 1

Topic :-

Straight Line

Given :-

Lines :-

x + y - 1 = 0

x - y - 1 = 0

To Find :-

Point of Intersection of given two lines.

Methodology :-

Method 1

Solve for value of 'x' and 'y'. Values will give coordinate of point of intersection i.e. (x, y).

Method 2

Draw the graph and observe the intersection point.

Solution :-

Method 1

Add both equations of given lines.

(x + y - 1) + (x - y - 1) = 0 + 0

x + y - 1 + x - y - 1 = 0

2x - 2 = 0

2x = 2

x = 2/2 = 1  

Put value of 'x' in any equation of line to get 'y',

x + y - 1 = 0

1 + y - 1 = 0

y = 0

Hence, point of intersection would be (1, 0).

Method 2

x + y - 1 = 0

Put x = 0,

0 + y - 1 = 0

y = 1

Mark point (0, 1) on the graph.

Put y = 0 ,

x + 0 - 1 = 0

x = 1,

Mark point (1, 0) on the graph.

Joining both points would represent line x + y - 1 = 0.

x - y - 1 = 0

Put x = 0,

0 - y - 1 = 0

y = -1

Mark point (0, -1) on thr graph.

Put y = 0,

x - 0 - 1 = 0

x = 1

Mark point (1, 0) on thr graph.

Joining both points would represent line x - y - 1 = 0.

Now, observing the graph we can say that (1, 0) is the intersection point of the given two lines.

Answer :-

The point of intersection of given two lines is (1, 0).

Note :

Refer to attachment for Graph of Method 2.

Red line represents x + y - 1 = 0 and

Blue line represents x - y - 1 = 0.