the sum of two numbers is 11. their product is 30. find the numbers. answer 5,6 represent the unknown by variables using let statements, translate into equationsusing variables. combine hem using substitution or elimination. answer the question by solvingand substituting state your final answer in compltete sentences

Solve this pair of equations. Let the two numbers by x and y

x + y = 11
xy = 30

x*(11-x) = 30

x^2 -11x + 30 = 0

That equation is easily factored.

You do the rest. We will critque your work if you wish.

To solve this problem, let's represent the unknown numbers with variables. Let's say the first number is 'x' and the second number is 'y'.

We are given two pieces of information:

1) The sum of two numbers is 11: x + y = 11.
2) The product of two numbers is 30: xy = 30.

Now, we can solve this system of equations using the substitution or elimination method. Let's start by using the substitution method.

From equation 1, we can express y in terms of x: y = 11 - x.

Substituting this value for y in equation 2, we have:

x(11 - x) = 30.

Expanding the equation, we get:

11x - x^2 = 30.

Rearranging the equation, we have:

x^2 - 11x + 30 = 0.

Now, we can factor this quadratic equation:

(x - 5)(x - 6) = 0.

This equation can be true only if either (x - 5) = 0 or (x - 6) = 0.

So, we have two possible solutions:

1) x - 5 = 0, which gives x = 5.
2) x - 6 = 0, which gives x = 6.

Now, substituting these values into equation 1 to find the corresponding y values:

For x = 5, y = 11 - 5 = 6.
For x = 6, y = 11 - 6 = 5.

Therefore, the two numbers are 5 and 6.

In conclusion, the two numbers that satisfy the given conditions are 5 and 6.