# Intersection of two functions

1. Apr 29, 2015

### Mrencko

1. The problem statement, all variables and given/known data
The problem ask for points of intersection of two functions
2. Relevant equations
1: 2x+y-4=0
2: (y^2)-4x=0

3. The attempt at a solution
My attempt of solution its in a picture attached below...
I get stuck in this two equations
1: ((y^2)/4)+(y/2)-2=0
2: square root(-4x)-2x+4=0
What. Can i do whit that two equations
I ve tried the square formula and given a weir and nonsense result

2. Apr 29, 2015

### SammyS

Staff Emeritus
No picture included.

Multiply first equation by 2 then add equations to eliminate x.

3. Apr 29, 2015

### Mrencko

This is the picture of my work

4. Apr 29, 2015

### Mrencko

5. Apr 29, 2015

### SammyS

Staff Emeritus
How do you get $\ y=\sqrt{-4x}\$ ? Specifically, where does that negative sign come from in under the radical ?

6. Apr 30, 2015

### HallsofIvy

Staff Emeritus
That was incorrect. Anyway, much simpler is your first suggestion: Multiply first equation by 2 then add equations to eliminate x.

Equivalently, multiply the first equation by 2, then write it as 4x= 8- 2y so that the second equation can be written $y^2- 8+ 2y= 0$ or $y^2+ 2y- 8= 0$.

7. Apr 30, 2015

### Mrencko

Thanks i will do that, but what is the point of multiply by 2? Dont change the integrity of the next equation?

8. Apr 30, 2015

### SammyS

Staff Emeritus
Multiplying an equation by 2 gives an equivalent equation. Right ?

If you want to use the method of substitution, it's better to solve one of the equations for x rather than for y. Then substitute that into the other equation. That way you don't take a square root.

Last edited: Apr 30, 2015
9. Apr 30, 2015

### Mrencko

10. Apr 30, 2015

### SammyS

Staff Emeritus
Solve it.

11. Apr 30, 2015

### Mrencko

What is thw diference between this and the above equation? Pictures i mean

12. Apr 30, 2015

### SammyS

Staff Emeritus
Maybe not much? I didn't like the $\ \sqrt{-4x\ }\$. Especially since x had to be positive.

What is your ultimate goal here?

13. Apr 30, 2015

### Mrencko

Find the x and y intersections, i think this is finally solved, but my only doubt, if is this is posible to solve trought this equation:((y^2)/4)=(4-y)/2

#### Attached Files:

• ###### 14304138321541924722937.jpg
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35.5 KB
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14. Apr 30, 2015

### SammyS

Staff Emeritus
Why not ?

15. Apr 30, 2015

### Mrencko

If i use the quadratic form whit that equation i get, irrational numbers

16. Apr 30, 2015

### SteamKing

Staff Emeritus
You shouldn't.