Finding Points of Intersection for Two Functions

[Mrencko]

Homework Statement

The problem ask for points of intersection of two functions

Homework Equations

1: 2x+y-4=0
2: (y^2)-4x=0

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[/B]

 

[SammyS]

Homework Statement

The problem ask for points of intersection of two functions

Homework Equations

1: 2x+y-4=0
2: (y^2)-4x=0

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[/B]

No picture included.

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

 

[Mrencko]

No picture included.

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

This is the picture of my work

 

[Mrencko]

This is the picture of my work View attachment 82799

 

[SammyS]

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

 

[HallsofIvy]

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

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.

 

[Mrencko]

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

 

[SammyS]

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

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.

 

[Mrencko]

 

[SammyS]

View attachment 82840

Solve it.

 

[Mrencko]

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

 

[SammyS]

What is the difference between this and the above equation? Pictures i meanView attachment 82841

Maybe not much? I didn't like the $\ \sqrt{-4x\ }\$. Especially since x had to be positive.What is your ultimate goal here?

 

[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

 

[SammyS]

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

Why not ?

 

[Mrencko]

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

 

[SteamKing]

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

You shouldn't.

Please show your calculations.

 

[Mrencko]

i went out for vacations, and somehow now its clear for my using the two metods and two equations, i am very grateful for the help, cheers guys :)