systems of equations

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moosie2323

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Coach M invests some money in two savings accounts, one earning 10% interest and the other earning 8% interest. Each account is compounded annually. If the total he invests is $6000 and his annual return is $564, how much does he invest in each account?

I need to use the information given to set up a system of two linear equations in two variables. How would I set it up?
 
Let x=amount invested at 10%

Then, 6000-x is the amount remaining at 8%.

We only need one equation.

\(\displaystyle .10x+.08(6000-x)=564\)

solve for x.
 
don't think that's right I would have to set up an linear equation like Example.
3x+4y=36
x-2y=-8
Then I would have to sole using cramer's rule. I just need to know how to set up the linear equations from the word problem.
 
The two equations are in the one I gave. Dissect it a little.

Cramer's rule?. Do you have to use that?.
 
yes i do it tells me to use the info to set up a system of two linear equations in two variables. Then use cramer's rule to solve the system.
 
x + y = 6000
8x + 10y = 56400 (from .08x + .10y = 564)

Now phone Cramer :wink:
 
Thanks that was helpful but I have one more and this time I have to set up a system of three linear equations in three variables.

Pam Wu has a coin purse that contains pennies, nickles, and dimes whose total value is $1.75. There are 35 coins in all, and the number pennies exceeds the number of nickels by 7. How many of each coin does she have in her coin purse?
 
moosie2323 said:
I think it has to be in the same form as the previous question with the x and y
Click to expand...
Huh? IT IS in the same form.
What difference(s) do you see?

I hope you DO know that p - n = 5 is same as 1p - 1n + 0d = 5
 
I see what you're saying but in the book examples they only use x and y. Here is an example from the book

3x+y-z=6
-x+5z=7
4y+z=-2

That's what they consider a system of three linear equations in three variables
 
moosie2323 said:
I see what you're saying but in the book examples they only use x and y. Here is an example from the book

3x+y-z=6
-x+5z=7
4y+z=-2

That's what they consider a system of three linear equations in three variables
Click to expand...

Ok...in the system of equations that Denis wrote for you, he used (I assume) the variable "p" to represent the number of pennies, the variable "n" to represent the number of nickels, and the variable "d" to represent the number of dimes. There is absolutely NOTHING WRONG with using variables other than x, y and z....in fact, many people find it easier to write the equations if the variables "look like" the names of the missing quantities in the problem.

However, if you feel you MUST use x, y and z (and there is absolutely no mathematical reason why you should HAVE to), simply re-define the variables....for example, you might let x = number of pennies, let y = number of nickels, and let z = number of dimes. Then use Denis's equations, substituting your newly-defined variables for the ones Denis used.
 
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