Question

What two numbers have sum of 5 and have a product of -450

Answer 1

Step-by-step explanation:

What are my two numbers if their sum is 5 and their product is 4?

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Let the two numbers be x and y .

Now with the given information, we can form two equations, (1) and (2):

x+y=5 —-(1)

xy=4 —-(2)

Method 1: Substitution

In this method, we express one variable in terms of another (in the first equation) and “substitute” that into the second variable to get a final equation in terms of one variable only. We then solve for that variable and then use that value to solve for the other variable.

Let’s see this method in action:

x+y=5 —-(1)

Now let’s express x in terms of y(ie. make x the subject of the equation, with x alone on one side and an expression in y on the other side)

x=5−y

Now that we have found x in terms of y, we “substitute” x into (2):

xy=4

(5−y)y=4

Simplifying the equation:

5y−y2=4

y2−5y+4=0

(here we have a quadratic in y)

We factor the equation:

y2−4y−y+4=0

y(y−4)−(y−4)=0

(y−4)(y−1)=0

Either y−4=0 Or y−1=0

Therefore solutions for y are 1 and 4.

When y=1,x=5−1=4

When y=4,x=5−4=1

Hence, the solutions (x,y) to this simultaneous equations is (4,1) and (1,4).