Question

3x+2y=4
x+3y=-1
solve using addition

Answer 1

are you sure you use addition? don't you mean substitution or elimination?

Answer 2

@amyamanda

Answer 3

it says addition

Answer 4

then just add the two systems together.

what is 3x+x?

Answer 5

4x

Answer 6

and 2y+3y? Good!, btw

Answer 7

5y

Answer 8

then 4+(-1)?

Answer 9

3

Answer 10

right so put it all together and you get... :)

Answer 11

so 4x+5y=3

Answer 12

right! good job :)

Answer 13

r u sure that's right, that doesn't seem right

Answer 14

why? is it not a choice, because as you solve by addition, addition means to add, so this should be your answer

Answer 15

unless i have misunderstood your question...

Answer 16

"Addition" does not stop you from multiplying by a + or - factor before you add. Essentially it would be elimination.

Answer 17

? I'm confused

Answer 18

so you would use elimination? hmmm i must have learned it differently

Answer 19

@mathmate does that mean that 4x+5y=3 is incorrect?

Answer 20

As far as I know, I would not accept 4x+5y=3 as the solution to a system of equations.

Answer 21

ok @mathmate could you please break down step by step for me

Answer 22

right i was just confused when she said solve by addition. However for this case, substitution seems more applicable

Answer 23

or is it just me? idk

Answer 24

The solution set to a system of two equations would typically (but not always) be
S=(x,y) where x,y are numbers.

Answer 25

Yes, substitution and elimination are both feasible.

Answer 26

However, elimination is a kind of addition, so that's what I suggest, not because it is simpler.

Answer 27

ok how do I use elimination?

Answer 28

Elimination means that you multiply one or both equations with certain numbers so that the coefficients of a variable are identical.
For example, if you multiply the second equation by -3, you will get
3x+2y=4
-3x-9y=3
Now you need to add the two equations and solve for y because the x's will cancel out when you ADD.

Answer 29

y=-1

Answer 30

@mathmate y=-1

Answer 31

Very good, now all you have to do is to put y=-1 into one of the original equations and solve for x.

Answer 32

x=2

Answer 33

independent equation because it only has one solution

Answer 34

Good observation!
Now the last step (whenever you solve a system of equations) is to put back the solution set into the original equations and see if they "work".
What is your solution set?

Answer 35

6-2=4
2-3=-1

Answer 36

Perfect, they match.
The solution set is S=(2,-1) i.e. x=2, y=-1, is that ok?

Answer 37

yup

Answer 38

ty!

Answer 39

yw!