# Finding point of intersection algebraically

• Feb 12th 2008, 10:44 AM
~NeonFire372~
Finding point of intersection algebraically
Another question for a test tomorrow that I don't understand... I know how to find the point of intersection for two lines on a graph easily but I don't understand how you do it algebraically and the teacher refuses to explain it to anyone again since we've already done it though I was absent that day.
• Feb 12th 2008, 11:01 AM
Jhevon
Quote:

Originally Posted by ~NeonFire372~
Another question for a test tomorrow that I don't understand... I know how to find the point of intersection for two lines on a graph easily but I don't understand how you do it algebraically and the teacher refuses to explain it to anyone again since we've already done it though I was absent that day.

you set them equal to each other.

say one line is y = 2x + 5 and the other is y = 3x - 1, then the (x-coordinate for the) point of intersection is given by:

2x + 5 = 3x - 1

do you see how that makes sense? we want to see where their y-values match up, and then match up the x-values at that point. if the x- and y-values are the same on both lines, it means it is a point they both pass through, and hence they intersect there
• Feb 12th 2008, 11:04 AM
~NeonFire372~
2x + 5 = 3x - 1

So I'd go:

2x -3x = 5 - 1
-1x = 4

... I'm really confused now. (Worried)
• Feb 12th 2008, 11:10 AM
Jhevon
Quote:

Originally Posted by ~NeonFire372~
2x + 5 = 3x - 1

So I'd go:

2x -3x = 5 - 1
-1x = 4

... I'm really confused now. (Worried)

that's because you did the wrong thing. first off, i'd move the x's to thee right hand side, to avoid the -x. it's no big deal really, but i like my math to look aesthetically pleasing.

so, 2x + 5 = 3x - 1 .............subtract 2x from both sides.

=> 5 = 3x - 1 - 2x ..............simplify

=> 5 = x - 1 ......................now add 1 to both sides

=> 5 + 1 = x ......................simplify

=> x = 6

thus we have found the x-coordinate for which the lines intersect. to find the y-coordinate, plug the x-value we found into either equation.

say we decided to use y = 2x + 5

plug in x = 6, we get:

y = 2(6) + 5

=> y = 17

say we decided to use y = 3x - 1

plug in x = 6, we get:

y = 3(6) - 1

=> y = 17 again, aha!

so when x = 6, y = 17

thus the point of intersection is (6,17)
• Feb 12th 2008, 11:14 AM
~NeonFire372~
Quote:

Originally Posted by Jhevon
that's because you did the wrong thing. first off, i'd move the x's to thee right hand side, to avoid the -x. it's no big deal really, but i like my math to look aesthetically pleasing.

so, 2x + 5 = 3x - 1 .............subtract 2x from both sides.

=> 5 = 3x - 1 - 2x ..............simplify

=> 5 = x - 1 ......................now add 1 to both sides

=> 5 + 1 = x ......................simplify

=> x = 6

thus we have found the x-coordinate for which the lines intersect. to find the y-coordinate, plug the x-value we found into either equation.

say we decided to use y = 2x + 5

plug in x = 6, we get:

y = 2(6) + 5

=> y = 17

say we decided to use y = 3x - 1

plug in x = 6, we get:

y = 3(6) - 1

=> y = 17 again, aha!

so when x = 6, y = 17

thus the point of intersection is (6,17)

The two simplify steps - I don't get why the 5 would be = to the rest of it and why then it would be changed to =x. (Worried)
• Feb 12th 2008, 11:20 AM
Jhevon
Quote:

Originally Posted by ~NeonFire372~
The two simplify steps - I don't get why the 5 would be = to the rest of it and why then it would be changed to =x. (Worried)

i did not change the 5 to x. i flipped the equation around. if i had simplified, i would have 6 = x, that looks weird, so i turned it around to say x = 6
• Feb 12th 2008, 11:24 AM
~NeonFire372~
But if you didn't simplify or flip anything around, how would it work?
• Feb 12th 2008, 11:29 AM
Jhevon
Quote:

Originally Posted by ~NeonFire372~
But if you didn't simplify or flip anything around, how would it work?

what do you mean. nothing would change if we write 6 = x as opposed to x = 6. that's saying the same thing. i don't see your confusion i'm afraid. i simplify to make things look nicer and easier to use. like writing 6 instead of 5 + 1. they are the same thing, but one is simplified...