Question

Solve this system of equations using the addition method.
3x-y=9
2x+y=6 Solve this system of equations using the addition method.
3x-y=9
2x+y=6 @Mathematics

Answer 1

5x + 0 = 15
x = 3
plug to the first equation
2.3 + y = 6
y = 0

Answer 2

so i would just add the numbers then divide

Answer 3

first add the equation 1 and 2 so that it will get rid of one of the variable
In this example, you got it easy because in equation 1 you have -y, and in equation 2 you have y, so the sum of these equations will get rid of y

Answer 4

in case you want to get rid of x first. then you would have to do the following:
multiply 1st equation by 2
multiply 2nd equation by -3 so that it would appear like this
6x ....
-6x
-------------
0x ......

Answer 5

im sorry im very confused..see im takin algebra online and dnt have a teacher so i have to take tests online and have no idea how to do them

Answer 6

ok so you have two equations and two variables which is x, y. They ask you to find those values of x, y so that when you plug them in to any equation, they have to be true. In this case if you plug x = 0 and y = 3. Both equations hold. That's how it goes anyways.

Answer 7

Now they asked you to use addition method which means. some how you have to add equation 1 and equation 2

Answer 8

3x-y=9
+
2x+y=6
----------
5x + 0 = 15
the new equation only has x now.
So you know what x is, just plug into any of the equations they gave you, you will get y value.

Answer 9

give me another problem, i'll explain in more details because this is problem is very simple.

Answer 10

ok 4a-5b=7
4a+5b=17

Answer 11

alright. this is also simple. Let's change to 4a + 5b = 7
2a + 3b = 9 instead.

Answer 12

now what do you do? I want to know how you do it, then I'll explain

Answer 13

i add 4a to 2a right

Answer 14

continue

Answer 15

then i add5b and3b

Answer 16

ok. but the new equation doesn't get rid of any variables right? so your stuck

Answer 17

you have to modify the original equations somehow so when adding you will get either 0x or 0y

Answer 18

look at this problem you gave me:
4a-5b=7
4a+5b=17
notice the -5b (1st) and 5b (2nd equation). when adding the result is 0b. that's why i said they gave you a simple problem. Just adding.

Answer 19

did you learn how to modify the equations yet? or just purely adding stuff?

Answer 20

no did learn to modify the equations

Answer 21

okay then please try to modify this one:
4a + 5b = 7
2a + 3b = 9

Answer 22

i cnt i dnt understand how to modify im sorry

Answer 23

let's try to modify so when adding I will get 0a ok?

Answer 24

i see first equation have 4a. the 2nd have 2a. ... I need to have some how to have 2nd equation to have -4a. Right?

Answer 25

ummm yes

Answer 26

you can do this by multiply 2nd equation by -2

Answer 27

what's the modified equation now?

Answer 28

ok the modified (2nd equation) becomes:
-4a -6b = -18

Answer 29

now you can add the first and the modified.

Answer 30

so then id add the 4a and 5b

Answer 31

no no. it's gonna be like this:
4a + 5b = 7
+
-4a -6b = -18
-----------------------
0a -b = -11

Answer 32

you only add the a and a... b and b not a and b.

Answer 33

o

Answer 34

so now you can solve for the b value. Once you have one variable solved, plug to any of the original equation, then bam. That's it

Answer 35

can you modify to get rid of b instead of a this time? it's a bit harder, but same method.
4a + 5b = 7
2a + 3b = 9

Answer 36

you have to modify both equations for b.

Answer 37

4a+2a right

Answer 38

yes what about b

Answer 39

5b+3b?

Answer 40

so you will get 6a + 8b = 16?

Answer 41

it doesn't get rid of b does it?

Answer 42

so i subtract

Answer 43

you need to get help from professor about this. But those problems you gave me. you can just add them directly without modifying anything.

Answer 44

you are not clear about the concept of adding.

Answer 45

one thing I can tell you that when adding you must get rid of one of the variables.

Answer 46

no im not im sorry thnks for tryin to help tho

Answer 47

i have to go home. sorry