Question

What is the point of interestion of graph of equation X + Y = 3 with the x- axis​

Answer 1

Step-by-step explanation:

Equation of x-axis is y = 0. Let the point of intersection of the graph of the equation x + y = 3 with the x-axis be (p, 0). Since (x, 0) lies on the graph, it satisfies the equation. Thus, the line x + y = 3 intersects x-axis at point (3, 0).

Answer 2

$x+y=3\\\implies 1\cdot x+1\cdot y+(-3)=0$

Which is of the form,

$Ax+By-3+C=0,\:\:where\:A=1, B=1\:and\:C=-3$

This equation represents a straight line

Equation of x-axis is, $0\cdot x +y=0$

Now, let us assume that the two straight lines intersect each other at a point (m, n)

$\\\implies (m,n) \:is\:a\:point\:on\:the\:first\:line\\\implies 1\cdot m +1\cdot n -3 =0\\\implies m+n=3\:\:\:(eqtn.\:1)$

Also,

$(m,n)\:is\:a\:line\:on\:the\:x\mbox{-} axis\\\implies 0\cdot m+n=0\\\implies n=0\:\:\:(eqtn.\:2)$

From eqtn. 1 and eqtn. 2, we get,

$m=3,n=0$

Therefore the graph of the given equation intersects with the x-axis at (3,0)