Question

Please help me with an addition formula problem!


Solve the system by the elimination method. Check your work.

2a + 3b = 6

5a + 2b - 4 = 0

Answer 1

Okay so your first step is to solve for one of the variable in one of the equations.

Answer 2

Then take whatever is on the other side of the equation and substitute it for the variable in the other equation

Answer 3

But I'm not sure how to do that.

Answer 4

Is it 2a + 3b = 6
6ab = 6
divide both sides by 6
ab = 1
???

Answer 5

@wio is reffering to the substitution method, the question requires the use of elimination.

Answer 6

Okay, I'm confused now.

Answer 7

Substitution and elimination are two different methods to solve systems of equations, which one do you want to use?

Answer 8

Let's use elimination.

Answer 9

2a + 3b = 6
5a + 2b - 4 = 0

By examining the two equations, we try and look to do something to one or both of them to make two of the values the same, so for example, if we multiply equation one by a factor of 5 and multiply eqn two by a factor of 2, we will get:

10a + 15b = 30
10a + 4b - 8 = 0

Notice how we have 10 in both of them

Answer 10

okay..

Answer 11

So can we just take out the 10 and leave a?

Answer 12

no... if we subtract the two equations, then we will get ride of a completely.

10a + 15b -30 = 0
- 10a + 4b - 8 = 0
--------------------
11b - 38 = 0

Answer 13

oh, ok

Answer 14

then we can solve for b right there.
11b - 38 = 0
11b = 38
b= 38/11

Sub that b value back into either of the equations to find a

Answer 15

ok

Answer 16

2a + 3b = 6....(1)
5a + 2b - 4 = 0 ...(2)
(2a + 3b = 6) * 2...(3)
(5a + 2b - 4 = 0) * 3...(4)
elimation:
(3) - (4)
a = ?
then substitude a = ? into (3) or (4) to find b.

Answer 17

ok, so a - 4

Answer 18

but 0 times any number is 0, so a = 0?

Answer 19

@baldymcgee6 is the answer 38/11,0?

Answer 20

do those answers solve the system?

Answer 21

No, they don't

Answer 22

but that's all I could come up with.

Answer 23

What do I do?

Answer 24

We must have done something wrong.. let me check

Answer 25

2a + 3b = 6
5a + 2b - 4 = 0

10a + 15b -30 = 0
- 10a +4b - 8 = 0
----------------------
11b -22 = 0

11b = 22
b = 22/11 = 2

Answer 26

my bad, sorry about that. Just a simply subtraction error there.

Answer 27

I think I've tried 2,0, but that didn't work..

Answer 28

@baldymcgee6 2,0 didn't work, should I try 0,2?

Answer 29

2a + 3b = 6
5a + 2b - 4 = 0

if b =2 and a = 0

2(0) + 3(2) = 6 TRUE
5(0) + 2(2) - 4 = 0 TRUE

Answer 30

Okay, so 6,0?

Answer 31

no, our answer is correct,
b =2 a = 0

Answer 32

do I put it in the order of 2,0, or 0,2?

Answer 33

they are not co-ordinate points, a=0, b=2

Answer 34

Well, that's indeed strange that it counted as wrong. I'll ask my teacher!

Answer 35

okay

Answer 36

@baldymcgee6 hey you got it right guys it was 0,2