Finding intersection points of a line and parabola

[bambino9]

hi everyone! I am new to this site and hope you can help me out a little :)

This is a homework question but am unsure how to do these types of equations

y = - x + 5
y = x² - 16 x + 59

x= and y= or x= and y=

could someone tell me how you go about doing these equations?

Thanks

 

[Integral]

The general method for this type of problem is to isolate one variable, then use the resulting equation in the second equation to solve for the single remaining variable.

Give it a try and show us what you are doing.

 

[greytomato]

another approach, given "easy" equations is to draw the equations on X,Y plane and see how many intersections you get. the number of intersection is the number of (x,y) answers you'll get.
i.e. if you're drawing shows no intersections this means you got no answer...

 

[Hootenanny]

another approach, given "easy" equations is to draw the equations on X,Y plane and see how many intersections you get. the number of intersection is the number of (x,y) answers you'll get.
i.e. if you're drawing shows no intersections this means you got no answer...

Yeah a rough sketch will show how many solutions you will have. As for solving equations graphically, that's something I hate . As intergral said, you would usually isolate one variable, then solve for that variable. Start by trying to make one equation from the two you are given.

 

[HallsofIvy]

hi everyone! I am new to this site and hope you can help me out a little :)

This is a homework question but am unsure how to do these types of equations

y = - x + 5
y = x² - 16 x + 59

x= and y= or x= and y=

could someone tell me how you go about doing these equations?

Thanks

Since y= both -x+ 5 and x²- 16x+ 59, them must be equal to each other: x²- 16x+ 59= -x+ 5. Solve that for x, then put those values into y= -x+ 5 to find the corresponding y.

 

[greytomato]

there will be equations fom which you cannot isolate X nor Y.
there is where the sketch comes in :)

 

[Hootenanny]

there will be equations fom which you cannot isolate X nor Y.
there is where the sketch comes in :)

Yeah I know, but I still hate sketching graphs...could be the fact that I can't draw...

 

[Integral]

Looks like we are talking to ourselfs on this one. The OP has not been back since the origianal posts.

Please refrain from further responses until the OP comes back.

 

[Integral]

Yeah I know, but I still hate sketching graphs...could be the fact that I can't draw...

A hand drawn plot? I thought everyone just used their calculator these days?

 

[Hootenanny]

A hand drawn plot? I thought everyone just used their calculator these days?

I'm still using a bog standard scientific calculator, only one step away from the abacus! If I want anything resembling an accurate plot I usually use autograph.

 

[HallsofIvy]

Where have you gone, bambino?