Math Help - intersection of lines

1. intersection of lines

How would you determine if lines intersected or not

if the lines were something like

y=-x-2

and

y=x^2+2-4

2. Well since you have two expressions involving x's and y's you can put them together.

$y=-x-2$ and $y=x^2+2x-4$ so $y=-x-2=x^2+2x-4$ by equating the y's.

So you need to solve $-x-2=x^2+2x-4$ to get the x co-ordinate. The y co-ordinate can then be found by substituting this x value into one of the two equations (they should give the same answer if you've done it right!).

3. Originally Posted by Showcase_22
Well since you have two expressions involving x's and y's you can put them together.

$y=-x-2$ and $y=x^2+2x-4$ so $y=-x-2=x^2+2x-4$ by equating the y's.

So you need to solve $-x-2=x^2+2x-4$ to get the x co-ordinate. The y co-ordinate can then be found by substituting this x value into one of the two equations (they should give the same answer if you've done it right!).
would i just collect like terms and factor or how would i solve that?

4. Exactly!

$
-x-2=x^2+2x-4
$

Here's the first step: $x^2+2x+x-4+2=0$.

5. Originally Posted by william
How would you determine if lines intersected or not

if the lines were something like

y=-x-2

and

y=x^2+2-4
As far as I know y = x^2 + 2x - 4 is not a line... Its a parabola

6. Originally Posted by Isomorphism
As far as I know y = x^2 + 2x - 4 is not a line... Its a parabola
AH YES! thank you i could simply graph both and see where they intersect,if anywhere

7. Simultaneous equations are faster than just graphing them.

What if you have two lines that intersect at (100,1000000)? It would be very hard to draw a graph for that!