The sum of two numbers is 12 the difference of the same is -4 formulate a system of equation and find the number

The numbers are a= 4 and b= 8.

Step-by-step explanation:

Let the unknowns number be a and b.

assume a>b.

As per the given condition: The sum of two number is 12 and the difference of the same is -4.

from the above conditions we have:

     ......[1]

       ......[2]

Now, adding equations, we will eliminate b leaving an equation in a that we can solve:

⇒ [1]+[2] gives;

or

Simplify:

Divide by 2 on both sides, we get

Simplify:

a=4

Substitute the value of a= 4 in equation [1] . to solve for b;

or

b= 12-4 =8

Therefore, the numbers a and b are 4 and 8

Given problem;

  Write and algebraic expression for the number of awards Tomi's band has won;

   Let the number of award Tomi's band has won = T

   Let the number of award All's band has won  = A

We know;

      Tomi's band has won twice as many awards as All's band.

       T = 2 x A

  T  = 2A

The algebraic expression is T = 2A