Find two numbers a and b whose sum a+b is -1 and whose difference a−b is 5.
I do not understand the question
a + b = -1
a - b = 5
a = -1 - b
Substitute:
-1 - b - b = 5
-2b = 6
b = -3
a - 3 = -1
a = 2
Well, it seems like a tricky math problem. Let's break it down. So, the sum of two numbers, let's call them a and b, is -1. And the difference between those two numbers, a minus b, is 5.
Now, we can use our comedy skills to solve this problem. So, if we add a and b and we get -1, it means one number must be positive while the other one is negative.
And if the difference between a and b is 5, it means they are pretty distant from each other. Imagine two numbers having an argument, constantly bickering about their differences!
Now, to find those numbers, let's imagine that a is the positive number and b is the negative one. So, a + b = -1. Now, we can solve this using our clown logic!
Since b is negative, let's imagine that b is a grumpy -3. Now we need to find a number that, when added to -3, gives us -1. Well, let's try -1! So, a + (-3) = -1, which means a = 2.
So, we've got our numbers! a = 2 and b = -3. The positive number, a, plus the negative number, b, equals -1. And the difference between a and b is indeed 5. I hope my silliness helps you understand the problem a bit better!
To find two numbers, a and b, whose sum is -1 and difference is 5, we can set up a system of linear equations.
Let's assign a variable to each number:
a = first number
b = second number
According to the given information:
a + b = -1
a - b = 5
To solve this system, we can use the method of substitution or elimination.
Method 1: Substitution
1. Solve one equation for one variable (in terms of the other variable).
From the first equation, solve for a:
a = -1 - b
2. Substitute the value of a in the second equation:
(-1 - b) - b = 5
Simplify the equation:
-1 - 2b = 5
Add 1 to both sides:
-2b = 6
Divide by -2:
b = -3
3. Substitute the value of b in the first equation:
a + (-3) = -1
Simplify the equation:
a - 3 = -1
Add 3 to both sides:
a = 2
So, the solution is:
a = 2
b = -3
Therefore, the two numbers are 2 and -3.
a = b + 5
a + b = -1
Substitute b+5 for a in the second equation and solve for b. Insert that value into the first equation to solve for a. Check by putting both values into the second equation.