Use multiplication with the addition-or-subtraction method:?

Question

4d - 5c = - 22
c - 2d = 5

I don't understand how to get the answer, because the variables in in different places instead of 4d being over 2d, its 4d over c. I know I have to multiply to get the same coefficients, but how do I get them to be equal like :

4d - 5c = - 22
2d - c = 5

Thanks for helping me! :D

Answer 1

First just multiply the second equation by 2. So you have 2c-4d=10. Then add it to the first equation 4d-5c+2c-4d=-22+10. Combine like terms to get -3c=-12. Thus c=4, which you substitute to find that d=-1/2.

What you should remember is that the position of the terms is irrelevant, -2d is -2d regardless of whether it's c-2d or -2d+c (but note that c-2d ≠ 2d-c). What is relevant is whether the d terms will cancel each other out when you add the equations together. In this case, they did not, so we multiplied the second equation by 2 to get the terms to that point (we can do this because we are doing the same thing to both sides of the equation). Then we added the equations, just as you are familiar with.

Answer 2

use the elimination method

Ok, you are trying to get one variable by itself right, so you will have to cancel one out. Let's cancel out the "c" variable since it has a positive and negative value "c" is positive and "-5c" is negavtive. First you must rearrange c-2d=5 so that the c's in the top and bottom problem line up, now the bottom problem is now -2d+c=5. It is still the same problem because the variables and numbers kept their signs. C still is positive as in the first proble,s. and "2d" still is negative in both problesms.

Ok so now you have

4d-5c=-22
-2d+c= 5

Now, since youa ree trying to cancel out the "c" variables, you need to multiply all of the bottom problem by 5, so you will have 10d+5c=25

So now both of your equasions are

4d-5c=-22
-10d+5c=25

You see how the -5c and 5c can cancel out now? now you c

Switch the problems around to make it easier to subtract, so now you have

-10d+5c=25
4d- 5c=-22

So your eqausion now turn to

-6d=3

that means d=-1/2

now substitute d into one of the problems in order to figure out c

I'll use this one:

c-2d=5

-2d=1

So the equasion states

c+1=5

THat means c=4

Now substitute c in for the other problem to see if both answers work


4d-5c=-22

4d=-2

-5c=-20

so the equasion states

-2-20=-22, so you know the answers are right.







Okay when I wrote this I didn't read all of your question, so I didn't know what you were really asking.


When you want to swich number around in an equasion, you can do it as long as the signs in front of them stay in front of them.

For example

-1+c=3

Is the same as

c-1=3

Because, see still has a positive sign "invisible but understood" in front of it, and "1" still has the "-" is front of it.


If this didn't help at all, I'm sorry I wasted your time, I just got carried away...

Answer 3

4d-5c=-22 ;c-2d=5=>5c-10d=25
adding -6d=3 so d=-1/2
substituting c=4