Problem: The sum of two numbers is 10. Their product is 21. Find the numbers.

Solution:

To solve this problem, we can use a system of two equations with two variables. Let x be the first number and y be the second number.

1. The sum of two numbers is 10.

x + y = 10

2. Their product is 21.

xy = 21

Now we can solve for one variable in terms of the other and substitute into the other equation.

1. Solve for x in terms of y from the first equation.

x = 10 - y

2. Substitute this expression for x into the second equation.

(10 - y)y = 21

3. Multiply out the left side of the equation.

10y - y^2 = 21

4. Rewrite the equation in standard quadratic form.

y^2 - 10y + 21 = 0

5. Factor the quadratic.

(y - 7)(y - 3) = 0

6. Solve for y by setting each factor equal to zero.

y - 7 = 0 or y - 3 = 0

y = 7 or y = 3

7. Substitute each value of y back into the equation x + y = 10 to find x.

If y = 7, then x = 10 - y = 3.

If y = 3, then x = 10 - y = 7.

Answer: The two numbers are 3 and 7.

The answer is 3 and 7 because
3+7=10
And
3×7=21
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