Working with simple addition and multiplication of positive and negative numbers. Have completed 59 of 60 problems on a worksheet, I am stumped by one of them. For example Two numbers are given 30 and 13, You must find two number multiplied together equal -30 and when added equal 13, simple enough two numbers are 15 and -2. Cant solve this on. Two numbers added must equal 1, but if multiplied equal -30, Help please.
hint:
what is +6 times -5
what is +6 plus -5
To solve the problem where the sum of two numbers is 1 and their product is -30, you can use a system of equations. Let's assign variables to the two numbers to make it easier to solve.
Let's call the first number x and the second number y. We know that the sum of these two numbers is 1, so we can set up the equation:
x + y = 1
We also know that their product is -30, so the second equation is:
x * y = -30
Now we can solve this system of equations using either substitution or elimination method. Let's use substitution:
From the first equation, we can isolate one variable in terms of the other. Let's solve for x:
x = 1 - y
Now we substitute this value of x into the second equation:
(1 - y) * y = -30
Expanding and rearranging, we get:
y - y^2 = -30
Rearranging further:
y^2 - y - 30 = 0
Now we have a quadratic equation. To solve this, we can factor or use the quadratic formula. Factoring, we have:
(y - 6)(y + 5) = 0
Setting each factor to zero, we get two possible solutions for y:
y - 6 = 0 or y + 5 = 0
Solving these equations, we find:
y = 6 or y = -5
Now we can substitute these values of y back into the first equation to find the corresponding values of x:
For y = 6:
x + 6 = 1
x = -5
For y = -5:
x + (-5) = 1
x = 6
So the two pairs of numbers that satisfy the given conditions are (x = -5, y = 6) and (x = 6, y = -5).
Therefore, the two numbers you are looking for are -5 and 6, or vice versa.