If the product of two numbers is 21 and the sum is 10, what are the two numbers?

Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

We will be using simultaneous equations to solve this problem.

Let's establish the two equations we will be using to solve this problem as displayed below:

Let number no. 1 = x

Let number no. 2 = y

Equation No. 1 -

x + y = 10

Equation No.2 -

xy = 21

To begin with, let's make ( x ) the subject in the first equation as displayed below:

Equation No. 1 -

x + y = 10

x = 10 - y

Next we will substitute the value of ( x ) from the first equation into the second equation yo solve for ( y ) as displayed below:

Equation No. 2 -

xy = 21

y ( 10 - y ) = 21

10y - y^2 = 21

10y - y^2 - 21 = 0

- y^2 + 10y - 21 = 0

- [ y^2 - 10y + 21 ] = 0

- [ y^2 - 7y - 3y + 21 ] = 0

- [ y ( y - 7 ) - 3 ( y - 7 ) ] = 0

- ( y - 7 ) ( y - 3 ) = 0

Option No. 1 -

y - 7 = 0

y = 7

OR

Option No. 2 -

y - 3 = 0

y = 3

Then we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ) as displayed below:

Equation No. 1 -

Option No. 1 -

x = 10 - y

x = 10 - ( 7 )

x = 3

OR

Option No. 2 -

x = 10 - y

x = 10 - 3

x = 7

FINAL ANSWER:

Therefore, the two numbers are: 7 and 3.

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