Need help solving for two variables: solve e(d)=c(x-b), d+c=-c for x/b

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kartoff

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The problem asks me to solve for x/b and gives me the following equations to do so:

1. e(d)=c(x-b)

2. d+c=-c

I am really lost and a step-by-step explanation would be greatly appreciated. Thanks in advance!
 
kartoff said:
The problem asks me to solve for x/b and gives me the following equations to do so:

1. e(d)=c(x-b) → e*d = c * b * (x/b - 1) ..... continue....

2. d+c=-c

I am really lost and a step-by-step explanation would be greatly appreciated. Thanks in advance!
Click to expand...
.
 
mmm4444bot said:
What method did you try? Substitution?

Please show whatever you tried, even if you think it's wrong. You might not be as lost as you think.
Click to expand...

this is what I have done so far:

1. ed=c(x-b)
2. ed/(x-b)=c


then I plugged in the c value into the second equation, so

d+(ed/(x-b)= -(ed/(x-b))

I don't know what I must do next or if I have messed up somewhere
 
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kartoff said:
this is what I have done so far:

1. ed=c(x-b)
2. ed/(x-b)=c
Click to expand...
Let's not number our steps because we've already numbered the given equations as 1 and 2. If you would like to label new equations, you need to start with 3.


then I plugged in the c value into the second equation, so

d + ed/(x-b) = -ed/(x-b)

You had mismatched grouping symbols, on the left-hand side of this equation.
I fixed it here, by removing unnecessary parentheses.

I don't know what I must do next or if I have messed up somewhere.
Click to expand...
Your algebraic steps are good, however, you divided each side by x-b.

We don't know anything about the values of x, b, c, d, and e (except that b≠0). If we divide by the expression x-b, then we've already eliminated the possibility that x and b are the same number because, if they were the same, then the expression x-b would be zero and we could not divide by it.

Well, it turns out that one possible solution for x/b occurs when x and b are the same number. So, your approach might miss it:

x/b=1 IF x=b, b≠0, and e=0 (c and d can each be anything, as long as c=-d/2)

That is one case. There are other cases because we have five unknowns but only two equations. We're not told how either c or d relate to x, b, or e.

At first, I had thought they wanted an expression for x/b in terms of c, d, e, and/or constants only. (My attempts at symbolic expressions for x/b each contained either symbol x or symbol b.)

We can express x/b in terms of x and e, OR we can express it in terms of b and e. Maybe that's what Subhotosh and Denis are thinking they want. Denis showed how to relate x, b, and e.

We can get to the same relationship, with your start. You now have:

d + ed/(x-b) = -ed/(x-b)

If you divide each side of this equation by d, you will eliminate d.

From there, you can solve for x or b, and substitute the result into x/b. :cool:
 
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kartoff said:
The problem asks me to solve for x/b and gives me the following equations to do so:

1. e(d)=c(x-b)

2. d+c=-c → d = 2c

I am really lost and a step-by-step explanation would be greatly appreciated. Thanks in advance!
Click to expand...


e(d)=c(x-b)

(e * d)/b = c*(x/b - 1)

(e * d)/(b * c) = x/b - 1

e * 2 * c/ (b * c) + 1 = x/b

x/b = 1 + (2*e/b)
 
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