Question

An unknown number b is 10 more than an unknown number k. the number b is also k less than 8. the equations to find k and b are shown below: b = k + 10 b = −k + 8 which is a correct step to find k and b? (1 point)

Answer 1

The value of k=-1 and b=9.

Explanation:

Given : An unknown number b is 10 more than an unknown number k. The number b is also k less than 8. The equations to find k and b are shown below:
`b=k+10,b=-k+8`

To find : Which is a correct step to find k and b?

Solution :

The correct steps to find the value of k and b of the equations are

Let
`b=k+10` ......(1)

`b=-k+8` ......(2)

Step 1 - Equation the value of b from both the equations,

`k+10=-k+8`

Step 2 - Add like terms,

`2k=-2`

Step 3 - Solve,

`k=-1`

Step 4 - Substitute k in equation (1),

`b=-1+10`

`b=9`

Therefore, The value of k=-1 and b=9.

Answer 2

Just add the two equations together.
2b = 18
b = 18/2
b = 9

9 = k + 10
9 - 10 = k
k = - 1