How to determine algebraically the points of intersection of lines. ?

Question

How to determine algebraically the points of intersection of lines. ?

Answer 1

Let me tell you by example;

consider the two lines have these equations :

Line a) Y=2X + 4

Line b) Y=5X - 8

Intersection point is a point that these lines meet eachother , so coordination of intersection point must be true in both equations, because on that point , both lines have same X and Y.

So, Now we have two linear equations and two unknown value, what must we do? we have to simply mix two equations and find out the values. how ?

In eqauation a , we can say: X= 0.5Y - 2 , right?

Now , we know X and Y in equation a and b are same, so we put the value of X above in equation b:

Y= 5X - 8  => Y=5(0.5Y - 2 ) -8 , OK?

Now , we can say

Y= 2.5Y -10 - 8 , get it?

so , we simply calculate that:

Y= 12

Great , Now we have value of Y , how can we calculate X? It is simple , put value of Y in either equation and calculate value of X

equation a ) Y= 2X +4 => 12=2X +4 => X= 4

So , Now we can say that Lines a and b meet eachother at point i

Xi= 4 and Yi=12

Wish you luck

Answer 2

plug the intersecting point back into the equation and if both equations balance, u solved it algebraically

Answer 3

lines has their equations, use the method of elimination or substitution