Just a question I have - I understand the how but not the why.

if I have two equations of the line:

2x-y=9 ... (1)

3x+4y=-14 ... (2)

I can solve this using the elimination method by multiplying equation (1) by 4 on both sides and thereby eliminating the y's when adding equation (2) to (1)

- easy enough.

BUT how does this work in finding the point of intersection? Wouldn't multiplying one equation by 4 change the line and therefore the point of intersection? That is wouldn't the value of x change since we are not doing anything to (2)?