Question

What are the two integers who’s sim is -7 and product is 6

Answer 1

⇒Let the two unknowns be x and y

It is said that their sum is -7 mathematically it can be written as

`x+y=-7`

Their product can be written mathematically as

⇒ x×y=6

`xy=-6`

As a results you can see that we have a system of equation that we have to solve and we can solve it by substitution

let us derive the third equation from the first equation by making x the subject of the equation

As a results we have x=-7-y

Now let us substitute the equation to the second equation .

`(-7-y)(y)=6\\-7y-y^(2) =6\\-y^(2) -7y-6=0\\-(y^(2) +7y+6)=0\\y^(2) +7y+6=0\\(y+6)(y+1)=0\\y+6=0\\\\or\\y+1=0\\y=-6\\\\or \\y=-1`

when y =-1

x=-7-(-1)

x=-7+1

⇒x=-6

When y=-6

x=-7-(-6)

x=-7+6

⇒x=-1

Note there was no need of finding the values of x

the two numbers are

-6 and -1