Question

Pleeaaassseee help ! :(

I'm having trouble with solving systems of two equations in two variables. It makes me feel dumb :( can someone please explain this example question for me?

Solve the system of equations using elimination.
a. -2x-3y=5
-5x+3y=40

Answer 1

First, do you know how to simplify
-3y + 3y ?

Answer 2

yes

Answer 3

you should get 0

Answer 4

okay, so i'd eliminate that first. then should i try to get it by itself in one equation and get x?

Answer 5

The other idea you need is
if you have an equation, and you add the *same value* to both sides
it will stay an equation (in other words, the left side = right side)

Answer 6

Here is a simple example

1+2 = 3 (this is an equation)
add 4 to both sides
1+2+4 = 3+4 (this is still true. if we simplify we get 7=7, which is true)

Answer 7

now for your problem. we are given
-2x-3y=5

left side equals the right side

we are also told
-5x+3y=40 (another equation)

Let's start with the first equation and add 40 to both sides. (It will stay an equation right?)

-2x-3y + 40 =5+40

now use the second equation, which says that 40 is the something as -5x+3y
(that is what -5x+3y=40 means, right?)

-2x-3y + -5x+3y = 5+40

simplify
we know -3y +3y is 0
-2x -5x + 0 = 45 (and 5+40 is 45)

now add -2x and -5x
what do you get ?

Answer 8

-7x

Answer 9

yes, and we should always write out the full equation
-7x= 45

divide both sides by -7

Answer 10

x=6.4 ish? or 45/7

Answer 11

you write
\[ \frac{-7 \cdot x}{-7} = \frac{45}{-7} \]
the -7/-7 on the left side is 1
\[ x = \frac{45}{-7} \]
or - 45/7

so you are correct, except it's negative.

Answer 12

opps ! yes sorry i forgot to add the negative sign ! Thanks for correcting me & thanks for helping !

Answer 13

what it one thing i should always try to do first when trying to solve the equation though?

Answer 14

I made it look complicated. Here's how people do it: Add the 2 equations:

-2x-3y=5
-5x+3y=40
-----------
-7x = 45

now solve for x. That is the "short-way" to do what I did up above.

Answer 15

Now you might be thinking... it was *awfully convenient* that the -3y + 3y=0
because otherwise, we would still have a "y" to confuse things.

Answer 16

oh okay! my teacher didn't really explain this very well, that looks simple. If there is still a "y" , what would u do with it?

Answer 17

if there is still a y, we are in trouble.

Answer 18

Lol. So in this type of equation, there should only be one variable?

Answer 19

*one variable left

Answer 20

which is why we *make it so the y's go away*

example:
-2x -1y=5
-5x+3y=40

now if do our trick, we still have x's and y's and that is not good.

but here is the idea (brilliant!)
multiply the top equation (both sides) by 3
3 times the left side and 3 times the right side (it's still an equation)

3(-2x -1y) = 3*5
distribute the 3: -6x -3y = 15

now we have
-6x -3y = 15
-5x+3y=40

and when we add the two equations, the y's go away.

Answer 21

oh okay! understandable. In the equations before this, using substitution, there was 2 answers; one for x and one for y . Now, using elimination there should only be one, correct?

Answer 22

there are two unknowns (the x and the y), and a complete solution has a number for both. but once you know what x is, we use either of the original equations, replace x with its number, and solve for y.

Answer 23

okay! Thank You!

Answer 24

If you want to see some examples, watch Khan's videos. For example,
here's a 3 minute example:
http://www.khanacademy.org/math/algebra/systems-of-eq-and-ineq/solving-systems-addition-elimination/v/addition-elimination-method-1