Question

How do I solve this system of equations algebraically? (Will give medal & fan)

10x + 4y = 24
-6x - 4y = 8

Answer 1

If I'm correct... your suppose to cancel y out 1st since it's easier to get x. so it will be 4x=-16

Answer 2

Divide it by 4 and you will get x which will be x=-4

Answer 3

Plug in x for any of those equations then subtract it from the sum

Answer 4

Like so, -6 x 4 = -24-4y=8

Answer 5

24+8 = 32

Answer 6

Wait, the most we can do is just move y to the other side, right? we can't just get rid of it. so it would either be 10x = 24 - 4y for the first one or -6x = 8 + 4y for the second one.. right?

Answer 7

Divide by -4 which would be -8

Answer 8

You have to get rid of one to find the 1st one

Answer 9

@phi

Answer 10

You can only do it if they cancel out. Which is why y was canceled out.

Answer 11

I just don't understand...

Answer 12

y= -8 x=-4

Answer 13

I don't know how to explain it better than that :\ Sorry if I wasn't any help

Answer 14

I graphed the system on a graphing calculator, so I know the solution is x = 8 and y = -14, I just don't know how to get it by doing the math

Answer 15

.... Well idk

Answer 16

10(8) + 4(-14) = 24
80 + (-56) = 24
24 = 24

Answer 17

-6(8) - 4(-14) = 8
-48 - (-56) = 8
8 = 8

Answer 18

I just still need to be shown how to solve it algebraically... as if i never graphed it.. for anyone who wants to help...

Answer 19

I don't know how to solve it algebraically, but I graphed it and the answer is (8, -14)

Answer 20

Lol, I just saw that you knew that already...

Answer 21

10x + 4y = 24
-6x - 4y = 8

You would first cancel out the 4y's to solve for x, then add the equations together. You would then have the equation 4x=32.

Answer 22

Once you have that you would then divide both sides by 4.

Answer 23

how do you cancel out the ys?

Answer 24

Then you take that number and one of the equations and plug it in for x.

Answer 25

Its simply adding 4y to -4y which equals 0

Answer 26

So then it would be -6 = 8 + 4y though, right?

Answer 27

you can't just add it to one side...

Answer 28

No, you want to get rid of one to solve for the other.

Answer 29

But... you can't just do something to one side and not the other.

Answer 30

Yes you can, its called elimination.

Answer 31

Let me show you....

Answer 32

I've always been taught that you can't do something to one side and not the other, not in algebra.

Answer 33

If you add 4y to one side, you have to add 4y to the other side of the equation as well.

Answer 34

10x + 4y = 24
-6x - 4y = 8

4y+(-4y)=0

10x=24
+ -6x=8

4x=32
X=8

Answer 35

Your eliminating so you can solve for x then you are going to use that answer to solve for y.

Answer 36

I just don't even.... I was never taught anything like that.

Answer 37

It will be much easier once you learn that. Then things become less confusing.

Answer 38

I just don't know if I'll get credit for showing work I was never taught...

Answer 39

But I do see how it works... sorta

Answer 40

You cant solve it by moving them to different sides.

Answer 41

Its literally impossible to do that.

Answer 42

Oh okay, I see now, I went through my notes and found something similar

Answer 43

Thank you

Answer 44

Your welcome! :)

Answer 45

I am sure they taught you two ways to solve these equations

one way is substitution. The other is elimination.
elimination (in my opinion) is easier, especially if you have more than 2 equations and 2 unknowns.

Answer 46

I already figured this problem out, I forgot about the other method but then found something similar in my notes after a little bit of digging. I do need help on a different problem now though.

Answer 47

10x + 4y = 24
-6x - 4y = 8

in this problem, right away I notice a +4y in the first equation and a -4y in the 2nd equation... that is a clue to use elimination.

Here is the idea: the left side of eq 1 is equal to 24
the left side of equation 2 is equal to 8
if we add the left sides of the equations, the sum will be 8+24= 32

so let's do that:
10x + 4y + -6x + -4y= 32
(we are doing this because we know 4y + -4y is 0, and y is gone!)
10x - 6x simplifies to 4x and we get
4x = 32
x= 8

now use either of the equations to find y