The sum of two integers is -7. the product of the integers is -18. what are the integers

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

STEP-BY-STEP SOLUTION:

We will be using simultaneous equations to solve this problem.

Let's first establish the two equations we will be using.

Let integer no. 1 = x

Let integer no. 2 = y

Equation No. 1 -

x + y = - 7

Equation No. 2 -

xy = - 18

To begin with, we will make ( x ) the subject in the first equation.

Equation No. 1 -

x + y = - 7

x = - 7 - y

Next we will substitute the value of ( x ) from the first equation into the second equation to solve for ( y ).

Equation No. 2 -

xy = - 18

y ( - 7 - y ) = - 18

- 7y - y^2 = - 18

- y^2 - 7y + 18 = 0

- [ y^2 + 7y - 18 ] = 0

- [ y^2 + 9y - 2y - 18 ] = 0

- [ y ( y + 9 ) - 2 ( y + 9 ) ] = 0

- ( y + 9 ) ( y - 2 ) = 0

y + 9 = 0

y = - 9

OR

y - 2 = 0

y = 2

Then we will substitute the value of ( y ) from the second equation into the first equation to solve for ( x ).

Equation No. 1 -

x = - 7 - y

x = - 7 - ( - 9 )

x = - 7 + 9

x = 2

OR

x = - 7 - y

x = - 7 - ( 2 )

x = - 9

FINAL ANSWER:

Therefore, the answer is:

x = 2

y = - 9

OR

x = - 9

y = 2

The two integers are 2 and - 9 or - 9 and 2.

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