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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