When you add the equations in (a) you get 7x+y=24.

When you subtract the equations in (b) you also get 7x+y=24.

That means to solve both systems you can work with the same equation. However that is not enough. We must have two equivalent equations. We found only one.

Notice however that in the (b) we can take the first equation and divide every term by 2. When we do this we get 4x-5y=13. That’s the first equation in (a).

So both systems can be solved by working with the same two equations. These are 5x-5y=13 and 7x+y=24. And since we have two equations and two unknowns (the number of equations matches the number of variables) there is only one solution — one x and y that would make both systems true — solve both systems.

Basically we showed the systems are equivalent!

3 0

3 years ago

11,046 as a decimal

andrew11 [14]

Answer:

It cant be converted to decimal or fraction while it is a integer

4 0

2 years ago

Find the sum of the geometrical equation -3 , 18 , -108 , if there are 7 terms

harina [27]

Hello from MrBillDoesMath!

Answer:

Sum = -119,962 ( I hope!)

Discussion:

Let's determine the pattern.

first term: -3

2nd term: (-3) * (-6) = 18 (multiply first term by -6)

3rd term: (18) * (-6) = -108 (multiply 2nd term by -6)

4th term : (-108)*(-6) = 648 ( etc)

5th term : (648)*(-6) = -3888 (etc)

6th term : (-3888)*(-6) = 23328 (etc)

7th term: (23328)*(-6) = -139967 (etc)

Sum = -119,962

A simpler way to do this is to use the formula for the sum of a geometric series to n terms. The series is

-3 Sum ( -6)^n n = 0, 1, 2, 3, 4, 5, 6

Regards,

MrB

P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

3 0

3 years ago