Question

Solve this system using elimination. Check your answer. 6x + 4y = 42 and -3x + 3y = -6

Answer 1

We need to eliminate the x or y. How would you do this when combining the two equations?

Answer 2

What happens if you multiply the second equation by 2 then combine with the first equation?

Answer 3

it's often nice to first simplify the equations if you can.
if you can divide each of the numbers (by 2 in the first equation, for example), do that first.
6x+4y=42
divide *every term, both sides* by 2
3x + 2y = 21
we could simplify the second equation
-3x +3y=-6
but notice what happens if we add the two equations.

Answer 4

can you write it down ?

Answer 5

Like this: 3x + 2y = 21 + -3x + 3y = -6

Answer 6

ok, but you add left side to left side and right side to right side

Answer 7

Im confused @phi

Answer 8

3x + 2y = 21
-3x + 3y = -6
-------------
<--- sum goes here

Answer 9

3x + -3x = 0
2y + 3y = 5y
21 + -6 = 15

Answer 10

ok, but put the answer below the lines, and write it as a new equation

Answer 11

Like this: 0 + 5y = 15

Answer 12

yes

Answer 13

you can simplify it because adding 0 can be ignored

Answer 14

there is more to do
so far you have
5y= 15 (I assume you know 0+5y simplifies to 5y)
now divide both sides by 5

Answer 15

5y / 5 = 15/5
y= 3

Answer 16

next, pick one of the equations you started with.
6x + 4y = 42
replace y with 3. solve for x. can you do that?

Answer 17

so like this: 6x + 4*3 = 42 right

Answer 18

yes

Answer 19

So, then the answer would come out to be X=5 correct

Answer 20

you can test x=5, y=3 in the *second* equation.
if they work, you found the x and y that "solves" the system

Answer 21

-3x + 3y = -6
test with x=5 and y=3
that means replace x with 5, and y with 3 and simplify
if you get -6=-6 it works

Answer 22

So 6*5 + 4*3 = 42
42=42

Answer 23

So its true

Answer 24

you have to check that they work for both equations. but, so far, so good

Answer 25

So for the other equation: -3x + 3y = -6 we replace x with 5 and y with 3 right

Answer 26

yes

Answer 27

-3*5 + 3*3 = -6
-6 = -6 True

Answer 28

that shows that x=5, y=3 or if we write it as an (x,y) pair, the point (5,3) is the answer

Answer 29

Yes, Thanks

Answer 30

if you have time, look over how we solved this.
it should make some sense.

Answer 31

Yeah, im checking how we solved this to take notes

Answer 32

if you have time, seee
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-systems-topic/cc-8th-systems-elimination/v/solving-systems-by-elimination
and the other videos in this section.

Answer 33

Ok, thanks