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

Quote:

Originally Posted by

**oldjonesy** 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)?

Nope. If you multiply EVERYTHING by a constant number, it does not change anything. It will still be the equation of the same line.

Suppose we have the equation:

$\displaystyle y = 3x + 5$

What happens if we multiply the equation by 4? We get:

$\displaystyle 4y = 12x + 20$

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.