Question

Question #40e89

Answer 1

6 & -9

Explanation:

Always when you get an algebraic form, try naming the unknowns in terms of x,y,z,... because it is going to be easier.

In your case 2 digits:
let us call the first x and the second y

"have a product of -54"
therefore,
`x*y=-54`

"have a sum of -3"
therefore,
`x+y=-3`

Now the substitution method will be used which is finding `x` in terms of `y` from one of the equations, and substituting its value in the other equation.

From the second equation,
`x+y=-3`
`x=-3-y`

Then substituting this value of `x` in the first equation:
`x*y=-54`
`(-3-y)*y=-54`

expanding the equation
`-3y-y^2=-54`

multiplying the whole function by -1
`3y+y^2=54`

putting the whole function on one side:
`y^2+3y-54=0`

Here we have to factorize the terms `y^2+3y-54`
We can see the it is of the form `y^2+ay+b`
Now we have two find two numbers that when multiplied give us -54 and when divided give us 3, which is going to be c and d
then the above equation will be factorized into the form
`(y+c)(y+d)=0`
After looking at it we see that c and d are -6 and 9.
so,
`(y+(-6))(y+9)=0`

so
`y+(-6)=0`

or
`y+9=0`

Thus by putting unknowns on one side and numbers on the other, we get that,

`y=6` or `y=-9`
applying these values of y in the first equation, we get that

`x=-3-y`

`x=-3-6=-9`

or

`x=-3-(-9)=-3+9=6`

Finally we see that these two numbers are 6 and -9