Question

can you help me with this one and let me know if I do this correctly?
5x+5y=-11
7x-3y=13
x=12
y=8
5(12)+5(8)=100
7(12)-3(8)=60
what do I need to do?

Answer 1

were the values of x and y given or did you find them out?

Answer 2

You need to review your work. Obviously x=12 and y=8 don't check out!

Answer 3

I am having trouble with this

Answer 4

Were you directed to use "elimination" or substitution to solve this.

Answer 5

elimination

Answer 6

Which one (x or y) do you want to eliminate.....your cholice.

Answer 7

I am not sure... This is where I guess I am getting confused

Answer 8

It doesn't matter, just pick one x or y.

Answer 9

y

Answer 10

Good choice. Now you want to make the coefficient (number) of y in each equation the same. You can multiply in this case, Multiply the first equation (every term) by 3 and in the second equation multiply it by 5. That will make the coefficient of y the same number (15)

Answer 11

5x+5y=-11 (1)
7x-3y=13 (2)

multiply (1) by 7 and (2) by -5
35x + 35y = -77 (3)
-35x + 15y = -65 (4)
add (3) and (4) to get
50y = - 142
y = -142/50
y = -71/25

substitute y = -71/25 in (1)

-71
5x + 5*----- = -11
25
71
5x - ----- = -11
5
multiplying throughout by 5

25x - 71 = -55
-55 + 71 16
x = -------- = ------
25 25

Answer 12

That is the first step in elimination. Your two equations should look like this:
15x + 15y = -33
35x - 15y = 65

Answer 13

Do you follow so far?

Answer 14

Harkirat has eliminated the x but we can continue with your choice.

Answer 15

Ok, I am lost

Answer 16

Next step is to add those two equations that we just developed.

15x + 15 Y =-33
35X - 15 y= 65
--------------------- Add.
50x = 32
Notice how y got eliminated and we can solve for x.

Answer 17

Did you get lost when we multiplied the first equation by 3. Or are you lost in why in the heck we decided to multiply it by 3 in the first place?

Answer 18

LOL Yeah why multiplied by 3... I think

Answer 19

Yes, a good question. We decided we wanted to eliminate y, (your choice and a good one I might add) We are instructed to use the elimination method. To eliminate y we must manipulate the two equations (legally of course!) so that y has the same coefficient. Then we will either add or subtaract y getting zero, or in effect eliminating y.

The coefficient of y in the first equation is +5 (5y)
the coefficient of y in the second equation is -3 (-3y)
We want to make them the same number and we can do that by multiplying the first by 3..........but to keep it legal, we must multiply every term by three or we destroy the balance of the equation. left = right

Same goes for the second equation except we multiply thru by 5
Now they are the same coefficient (15) one + and one is a minus. Clear

Answer 20

ah I think I understand it better now

Answer 21

Now we can just add and eliminate y getting 0y

15x +15y=-33
35x - 15y =65
--------------- Adding to eliminate y
50 x +0y =32
50x=32
x=32/50=16/25
same value harkirat got for x.

Answer 22

Please review harikart's work and think about this and it will began to make sense.

Answer 23

so an ordered pair would look like this 32/50,16/25?

Answer 24

Let me look at harkirat's work . Harkirats shows a value of y at -71/25. So the ordered pair would be (16/25, -71/25).

I haven't doublechecked his work but just lookin it seems o.k.

Answer 25

You can verify by substituting for 16/25 for x and solving for y. Hopefully you will come up with the same.

Answer 26

ok, I am going to try this one
5x+3y=-11
7x-2y=17
I am going to eliminate Y and solve for X (or at least I am going to try)

Answer 27

5x+5y=-11 Original equation.
5(16/25) +5y=-11 Substituting 16/25 for x.
80/25 +11 =-5y

80 275
---- +------ =-5y
25 25

355
---- = -5y
25
355 -1
y = ---- x ----- =-71/25
25 5

Answer 28

2(5x + 3y = -11)---->10x + 6y = -22
3(7x - 2y = 17)------>21x - 6y = 51
31x = 29
x = 29/31