First, you solve for m by adding the equations.
m+n=100
+ m-n=30
--------------
2m=130
m=65
Now plug in 65 for m into one of the original equations
65+n=100
n=35
You can double check by plugging them both in:
65+35=100 and 65-35=30
Hope that helps.
8:38 is the time it was 32 minutes ago
16+5x =8x-5
Reorder the terms
16+5x = -5+8x
Solving for variable for x
Move all terms containing x to the left, all other terms to the right.
Add -8x to each side of the equation.
16+ -3x = -5 + 8x + -8x
Combine like terms: 5x + -8x=-3x
16+-3x = -5 + 8x + -8x
Combine like terms: 8x + -8x = 0
16+-3x = -5 + 0
16+ -3x = -5
Add -16 to each side of the equation
16+-16 + -3x = -5 + 16
Combine like terms: 16+ -16 = 0
0 + -3x =-5 + -16
-3x = -5 + -16
combine like terms: -5 + -16 = -21
-3x = -21
Divide each side by -3
x=7
The answer of x=7, because 7+2=9
Recall the identity,
(link to proof in the comments)
so that the required sum has a value of
Recall another identity,
which means
Then the sum's value reduces to 1/2.