* Need help with Finding the point of Intersection - Thanks

That's why we chose to solve L for y, so we could plug it into M to get an equation with only x'sx + 2x - 8 = 7Yes, that is correct. Now solve for x. Combine like terms on the left side and then isolate x by dividing both sides by the coefficient of x. You should get x = 5.Now, to find the corresponding y value, plug x = 5 into the equation for L: y = x - 4. That gives you y = 5 - 4 = 1.Therefore, the point of intersection for the two lines is (5,1).In summary, to find the point of intersection between the lines
  • #1
nukeman
655
0
* 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

 
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  • #2


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.
 
  • #3


Thanks,
 
  • #4


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
 
  • #5


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.)
 
  • #6


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?
 
  • #7


nukeman said:
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.
 
  • #8


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?



HallsofIvy said:
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.
 
  • #9


nukeman said:
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
 
  • #10


nukeman said:
so, x+ 2(x- 4)= 7
what do i do with this? I am solving for y correct?
No, you're solving for x.
 

FAQ: * Need help with Finding the point of Intersection - Thanks

1. How do I find the point of intersection?

To find the point of intersection, you will need to have two equations with two variables. Then, you can use algebraic methods such as substitution or elimination to solve for the values of the variables at the point of intersection.

2. What if my equations are in standard form?

If your equations are in standard form, you will need to first convert them into slope-intercept form by solving for y. Then, you can follow the same steps as in the previous question to find the point of intersection.

3. Can I use a graphing calculator to find the point of intersection?

Yes, you can use a graphing calculator to find the point of intersection. Simply input both equations into the calculator and use the "intersect" function to find the coordinates of the point of intersection.

4. What if my equations do not have a point of intersection?

If your equations do not have a point of intersection, it means that they are parallel and will never intersect. This can also occur if the equations represent the same line, resulting in infinite points of intersection.

5. How can I check my answer?

You can check your answer by plugging in the coordinates of the point of intersection into both equations. If the equations are true for those coordinates, then you have found the correct point of intersection.

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