Step-by-step explanation:
I understand it! Â (But I'm a high school math teacher so it might be unfair!) ; )
Anyway you have 2 numbers. Â You don't know what they are so we will call them x and y. Â Our first statement says that these numbers multiply to equal 120. Â So that first equation is
xy = 120
Our second statement says that they add to -22. Â So that second equation is
x + y = -22
Now we need to find the 2 numbers. Â We have 2 unknowns, x and y. Â That means that we have to have 2 equations. Â No more than 2 no less than 2. Â Solve the first equation for y. Â It doesn't matter which equation you pick and which variable you choose to solve for. Â If you do the work correctly, you will get the correct answers either way. Â Solving the first equation for y gives you:
Now tht we have a value for y, we can use the substitution property of equality to sub that value into the second equation for y:
Instead of finding a common denominator, we are going to eliminate x in the denominator altogether. Â Do this by multiplying everything by x to get
Get everything on one side of the equals sign and factor:
Because 12 * 10 = 120 and 12 + 10 = 22, our factors are 12 and 10:
Use factoring by grouping now. Â
From the first set of parenthesis you can factor out an x, and from the second set you can factor out a 10:
x(x + 12) + 10(x + 12) = 0
Now factor out the common x + 12 to get a factored quadratic:
(x + 12)(x + 10) = 0
By the Zero Product Property, either x + 12 = 0 or x + 10 = 0. Â Solving both for x gives you x = -12 or x = -10.
If x = -12, then
-12 + y = -22 so
y = -10
If x = -10, then
-10 + y = -22 so
y = -12.
The combinations of x and y are:
If x = -12, y = 10
If x = -10, y = -12
It doesn't matter which one is which. Â They are not asking you to specifically define x and y. Â They are asking you to find the numbers, and you did!