# Thread: A Variety Of Equations

1. ## A Variety Of Equations

Please solve and explain how these are solved.

Please solve and explain how these are solved.
Hi,

to Q1:

the brackets are not necessary. Collect like terms:

7t^(-6)*(-3)t^(-3)*c^(-3) = -21t^(-9)*c^(-3)

to Q3.:

11x + 6y = 153
156 = -3y + 10x ==> 156 - 10x = -3y ==> -312 + 20x = 6y

Now plug in the term for 6y into the first equation:

11x + (-312 + 20x) = 153

31x = 465

x = 15 plug in this value into the second equation to calculate y:

6y = -312 + 20*15 = -12
y = -2

EB

3. 7t^(-6)*(-3)t^(-3)*c^(-3) = -21t^(-9)*c^(-3)

How did you do that? -6* -3 -3* -3 = -21
I got -15

Solve using the elimination method.

. . 11x + 6y .= .153
. . 156 .= .-3y + 10x

We have: .11x + 6y .= .153 . [1]
. . . . . . . .10x .- 3y .= .156 . [2]

Multiply [2] by 2: .20x - .6y .= .312
. . . . . . Add [1]: .11x + 6y .= .153

. . And we have: .31x = 465 . . x = 15

Substitute into [1]: .11(15) + 6y .= .153 . . y = -2

7t^(-6)*(-3)t^(-3)*c^(-3) = -21t^(-9)*c^(-3)

How did you do that? -6* -3 -3* -3 = -21
I got -15
Hello,

you have to calculate the product of powers. Therefore you must use all rules concerning the calculations with powers.

I've attached a screen-shot of the transformation. Maybe this helps a little bit further.

EB

6. Thanks. That completes the picture.