# Thread: Finding points of intersection help for equations.

1. ## Finding points of intersection help for equations.

I have two graphs:
2x - 3y = 13

5x + 3y = 1

So I am assuming I need to get these two graphs in standard notation. So for the first equation; 2x - 3y = 13, I set it -3y = -2x + 13/-3 giving me y = 2/3x - 13/3.

For the second equation 5x + 3y = 1; I set it to 3y = -5x + 1 giving me y = -5/3x + 1/3

So the two equations I have so are

y = 2/3x - 13/3 and
y = -5/3x + 1/3

So how can I find the points of intersection from these two equations?

cheers.

2. Originally Posted by ipatch
I have two graphs:
2x - 3y = 13

5x + 3y = 1

So I am assuming I need to get these two graphs in standard notation. So for the first equation; 2x - 3y = 13, I set it -3y = -2x + 13/-3 giving me y = 2/3x - 13/3.

For the second equation 5x + 3y = 1; I set it to 3y = -5x + 1 giving me y = -5/3x + 1/3

So the two equations I have so are

y = 2/3x - 13/3 and
y = -5/3x + 1/3

So how can I find the points of intersection from these two equations?

cheers.
add the equations, term for term ...

2x - 3y = 13

5x + 3y = 1
------------
7x = 14

x = 2

sub 2 for x in either equation and solve for y

3. Originally Posted by skeeter
add the equations, term for term ...

2x - 3y = 13

5x + 3y = 1
------------
7x = 14

x = 2

sub 2 for x in either equation and solve for y
So when I plug in x for the first equation I get x = 2 and y = -3.
When I plug in x for the second equation I get x = 2 and y = 3.

So with that being said, do I have two intersection points one at (2, -3) and another at (2, 3) ?

cheers

4. Originally Posted by ipatch
So when I plug in x for the first equation I get x = 2 and y = -3.
When I plug in x for the second equation I get x = 2 and y = 3. this is incorrect, try the 2nd equation again.

So with that being said, do I have two intersection points one at (2, -3) and another at (2, 3) ?

think! ... how can two lines intersect at more than one point?
...

5. yeah i made a syntax error in my addition/subtraction, it is just one point. thanks for the FYI.

cheers