Question

I need some help solving these problems through elimination.

1) 4x+3y=-1
2x+5y=3
2) 12x-5y=9
3x-8y=-18

Answer 1

Is that the intersection of 4 lines? or 2 seperate questions?

Answer 2

2 seperate questions. If yiu can guide me through the first, maybe I can get the second?

Answer 3

elimination just means that we modify one equation thru multiplication in order to find a value that can cancel out a variable in the other equation.

Answer 4

4x+3y=-1
2x+5y=3 <- we can multiply this by -2 to get: -4x
should we?

Answer 5

Ok..

Answer 6

4x+3y=-1
(2x+5y=3) (-2)


4x +3y =-1
-4x-10y =-6 <-- now we add them together
-------------

Answer 7

So would y be -1

Answer 8

4x +3y =-1
-4x-10y =-6
------------
0 -7y = -7 <-- now we solve for y

y = 1 is correct

Answer 9

not -1. 1?

Answer 10

ok. got it

Answer 11

Since y = 1, we can use that to find "x" in the equations...

Answer 12

Do I just plug the y into one of the equations? or both?

Answer 13

either one is fine; they both meet at a specific point if they are not parallel lines; and that point has y=1 in common; so use it in any of them to find the common x value

Answer 14

Ok, so if I plug it into the first equation I got x=1 is rhat right?

Answer 15

-1

Answer 16

-1 is good to me :) this is a generic setup so dont be fooled by the position of the solution in my graph.....

Answer 17

Oh... thanks, but thankfully my teacher isnt making us graph :)

Answer 18

You see where the lines cross they have x and y in common right?

Answer 19

Yes, I do see that.

Answer 20

the solution to a set of equations is "where the lines have X and Y in common". Or at a single point.

Answer 21

Thanks for your help. I want to see if I can get the answer to the second one on my own. If I need help will you be around for a few?

Answer 22

i should be... :)

Answer 23

Which one should I try to cancel out? Does it matter?

Answer 24

doesnt matter; pick one and run with it :)

Answer 25

YAy... I think I got it (3,3)
Can you help me with this one or tell me if I'm right. This one is using subsitution.

6x-y=5
y=11x I got x=-5
y=-55
I dont think its right?

Answer 26

6x - 11x = 5

-5x = 5

x = -1

Answer 27

since y = "11x" we substitute that value into the other equation:

6x -y = 5

6x - (11x) = 5 ...and solve

Answer 28

Thank you. I see where I went wrong.