Question

Solve for a.
4a + 5b = 11
b = 3a - 13
When I did this, I got 4, but that isn't an answer choice. Did I do something wrong?

Answer 1

4a + 5b = 11

4a + 5(3a - 13) = 11 ... replace b with 3a - 13

4a + 15a - 65 = 11

keep going to solve for 'a'

Answer 2

Mind you, one of the answer choices was "None Of These."

Answer 3

I'm getting a = 4 as well (just worked on it)

Answer 4

so there's possibly a typo

Answer 5

I just wanted to check if I was correct X3
I have serious problems with these kinds of problems. Thank you c:

Answer 6

definitely something to bring up with the teacher because s/he will know how to fix it

Answer 7

and you're doing great, so keep up the good work

Answer 8

Thank you. Would you mind helping me with a couple of others? After awhile I will get it, I promise! XD

Answer 9

sure I'd love to help you out


what's your question?

Answer 10

I'm sure you will catch on quickly, so no worries

Answer 11

Solve for c.
2/3c - 1/3d = 2
1/5c + 1/10d = 1

When I did it I got d = 3 and c=9/2

Answer 12

that's a bit off, but close though

Answer 13

the first thing you can do is get rid of all the fractions (since fractions tend to complicate things)

Answer 14

the common denominator in the first equation is 3

so if you were to multiply EVERY term by 3, you would cancel out the fractions

2/3c - 1/3d = 2

3*(2/3c) - 3*(1/3d) = 3*2

6c/3 - 3d/3 = 6

2c - d = 6

Answer 15

see how I did that?

Answer 16

Yeah. That makes sense. You did it to keep the whole equation proportional, right?

Answer 17

exactly, to balance everything out, I multiplied both sides (or every term) by 3

Answer 18

how can you use this trick to simplify the second equation?

Answer 19

Multiply everything by 10

Answer 20

to get 2c + d = 10

Answer 21

very good, you're a total pro at this

Answer 22

we have gone from this system of equations

2/3c - 1/3d = 2
1/5c + 1/10d = 1


to this system (which is equivalent)

2c - d = 6
2c + d = 10

Answer 23

now we could isolate one variable and use substitution, but we can use elimination and get the job done faster

why? because we have a -d term in the first equation and a +d term in the second equation. They add to -d+d = 0d =0, so this means that adding the two equations means the 'd' terms go away. This leaves us with just 'c' and we can solve for it


so add the equations to get

2c - d = 6
+ 2c + d = 10
------------
4c + 0d = 16


So we now know that 4c = 16

Answer 24

so c would be 4

Answer 25

yep you got it

Answer 26

Thank you very much x3

Answer 27

glad to be of help