x+y=97
x-y=19
add them up:
2x = 116
x = 58
sub that into the first equation to find y
x-y=19
add them up:
2x = 116
x = 58
sub that into the first equation to find y
B-L=19
the L cancel out, add the b together to get 2b
add 97 and 19 together
2b=116
divide both side by 2
b=58
plug 58 in any two equation for b
58+y=97
minus 58 from both sides
y=39
If the sum of their ages is 97 and the difference is 19, we can set up a good ol' math equation. Let's call the two mysterious ages x and y, assuming x is greater than y:
x + y = 97 (Equation 1)
x - y = 19 (Equation 2)
Now, let's do some magic to solve this conundrum. We can add Equation 1 and Equation 2 together:
2x = 116
Dividing both sides by two, we find:
x = 58
If x is 58, we can substitute it back into Equation 1:
58 + y = 97
Subtracting 58 from both sides, we have:
y = 39
Voila! The ages of these mystery people are 58 and 39. I hope this math circus brought a smile to your face!
Let's say the ages of the two individuals are represented by variables, such as "x" and "y".
1. The sum of their ages is 97:
x + y = 97
2. The difference of their ages is 19:
x - y = 19
To solve this system of equations, we can use the method of elimination or substitution.
Method 1: Elimination
By adding the two equations together, we can eliminate one variable:
(x + y) + (x - y) = 97 + 19
2x = 116
Dividing both sides by 2 gives us:
x = 58
Now, substitute the value of x back into one of the original equations:
58 + y = 97
Subtract 58 from both sides:
y = 39
So, the ages of the two individuals are 58 and 39.
Method 2: Substitution
You can solve the system of equations by substituting one variable in terms of the other:
From equation 2, we can express x in terms of y as:
x = y + 19
Now substitute this expression for x in equation 1:
(y + 19) + y = 97
Combine like terms:
2y + 19 = 97
Subtract 19 from both sides:
2y = 78
Divide both sides by 2:
y = 39
Now substitute the value of y back into the expression for x:
x = 39 + 19
x = 58
So, the ages of the two individuals are 58 and 39.