Find two integers whose sum is 2 and whose difference is 8.
find two integers whose sum is 2 and whose difference is 8
a = first integer
b = second integer
a + b = 2
a = 2 - b
a - b = 8
2 - b - b = 8
2 - 2 b = 8
- 2 b = 8 - 2
- 2 b = 6
b = 6 / - 2
b = - 3
a = 2 - b
a = 2 - ( - 3 )
a = 2 + 3
a = 5
Let's call the two integers x and y.
According to the problem, the sum of these two integers is 2, so we can write the equation:
x + y = 2
The difference between the two integers is 8, so we can write another equation:
x - y = 8
To find the values of x and y, we can solve these two equations simultaneously using either substitution or elimination method. Let's use the elimination method.
We can add the two equations together to eliminate the y variable:
(x + y) + (x - y) = 2 + 8
2x = 10
Dividing both sides of the equation by 2, we get:
x = 5
Substituting this value back into one of the original equations, we can solve for y:
5 + y = 2
y = 2 - 5
y = -3
So, the two integers that satisfy the given conditions are 5 and -3.
To find two integers whose sum is 2 and whose difference is 8, we can use a system of equations.
Let's call the two integers x and y.
From the given information, we can set up the following equations:
Equation 1: x + y = 2 (sum is 2)
Equation 2: x - y = 8 (difference is 8)
To solve this system of equations, we can use the method of substitution.
Let's start by solving Equation 1 for x:
x = 2 - y
Now, substitute the value of x in Equation 2:
2 - y - y = 8
Simplify the equation:
2 - 2y = 8
Subtract 2 from both sides:
-2y = 6
Divide both sides by -2:
y = -3
Now substitute the value of y back into Equation 1 to find x:
x + (-3) = 2
x - 3 = 2
x = 2 + 3
x = 5
Therefore, the two integers are 5 and -3, since their sum is 2 (5 + (-3) = 2) and their difference is 8 (5 - (-3) = 8).