Two rational numbers with the sum of 1, product of -6/25 and quotient of -6.

( I have been working on this for a long time but I can't figure it out!)

To find the two rational numbers that satisfy the given conditions, we can set up a system of equations.

Let's assume the two rational numbers are x and y.

Given that the sum of the numbers is 1, we can write the equation:

x + y = 1 ----(1)

Given that the product of the numbers is -6/25, we can write the equation:

xy = -6/25 ----(2)

Given that the quotient of the numbers is -6, we can write the equation:

x/y = -6 ----(3)

Now, we have a system of three equations (equations 1, 2, and 3) with two variables (x and y). We can solve this system of equations to find the values of x and y.

To solve the system of equations, we can follow these steps:

Step 1: Solve equation 3 for x in terms of y.

From equation 3, we have: x = -6y.

Step 2: Substitute the value of x from step 1 into equations 1 and 2.

Substituting x = -6y into equation 1, we get:

-6y + y = 1
-5y = 1
y = -1/5

Substituting y = -1/5 into equation 2, we get:

x(-1/5) = -6/25
x = 6/5

So, the two rational numbers that satisfy the given conditions are x = 6/5 and y = -1/5.