Solving simultaneous equations
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)?
Re: Solving simultaneous equations
Nope. If you multiply EVERYTHING by a constant number, it does not change anything. It will still be the equation of the same line.
Originally Posted by oldjonesy
Suppose we have the equation:
What happens if we multiply the equation by 4? We get:
So to plot the line, just find the x-intercept and the y-intercept and draw a line that goes through those 2 points.
Have you tried plotting them? You'll notice that they're the same line.