* Need help with Finding the point of Intersection - Thanks

[nukeman]

* Need help with "Finding the point of Intersection" - Thanks

Homework Statement

Can someone please explain how I would solve this: As in find the pair of the given lines point of intersection.

L: x - y = 4
M: x + 2y = 7

Now, Do i have to turn these into slope intercept ?

I know L: in slope intercept would be y = -x - 4 correct? or is it y = x + 4
But M I am having trouble with.

Im just having a hard time with this question. Can someone quickly run through the steps to find point of intersection?


Thanks, I really appreciate it!

Homework Equations

The Attempt at a Solution

 

[eumyang]

No, you don't have to rewrite the equations into slope-intercept form. Finding the point of intersection is the same as finding a value for x and a value of y that satisfies BOTH equations. You already did a similar problem in this thread:
https://www.physicsforums.com/showthread.php?t=432810
You solved using substitution in that thread. Do the same here.

BTW, although it's not needed, I see that you rewrote L into slope-intercept form. y = -x - 4 is not correct. Neither is y = x + 4.

 

[nukeman]

Thanks,

 

[nukeman]

I still can't get this question:

L: x - y = 4
M: x + 2y = 7

it says the ansewr is 5,1 - but ihave no idea how they got that

 

[eumyang]

I don't understand why you don't get it. You were able to solve the system using substitution in your previous thread. Like I said, do the same here. Start by solving one of the equations for one of the variables. (I would take the L equation and solve for x.)

 

[nukeman]

There must be something I am missing, because I keep getting the wrong answer

L: x - y = 4
M: x + 2y = 7

lets solve L first.

So, L turns into y = x-4 ... correct?

Then do I plut that into

(x - 4) + 2y = 7

Now this is where I get messed up. can u help me out this this next step please?

 

[HallsofIvy]

There must be something I am missing, because I keep getting the wrong answer

L: x - y = 4
M: x + 2y = 7

lets solve L first.

So, L turns into y = x-4 ... correct?

Yes, that is correct.

Then do I plut that into

(x - 4) + 2y = 7

Now this is where I get messed up. can u help me out this this next step please?

You don't replace "x" with that! y= x- 4 so you replace y with x- 4! That leaves an equation that has only x in it. x+ 2y= 7 becomes x+ 2(x- 4)= 7.

Another way to do this would be to subtract the first equation from the second:
(x+ 2y)- (x- y)= 7- 4. The two "x"s cancel leaving an equation for y.

 

[nukeman]

so, x+ 2(x- 4)= 7

what do i do with this? I am solving for y correct?

so, do i go,

x + 2x - 8 = 7

can u help me out here? am i correct, what's next step?

Yes, that is correct.


You don't replace "x" with that! y= x- 4 so you replace y with x- 4! That leaves an equation that has only x in it. x+ 2y= 7 becomes x+ 2(x- 4)= 7.

Another way to do this would be to subtract the first equation from the second:
(x+ 2y)- (x- y)= 7- 4. The two "x"s cancel leaving an equation for y.

 

[JonF]

so, x+ 2(x- 4)= 7

what do i do with this? I am solving for y correct?

so, do i go,

x + 2x - 8 = 7

can u help me out here? am i correct, what's next step?

Bring all your variables to one side of the equal sign, numbers to the other

 

[Mark44]

so, x+ 2(x- 4)= 7
what do i do with this? I am solving for y correct?

No, you're solving for x.