Help me with this math question?

Question

The sum of two numbers is 82. Their difference is 24. Write a system of equations that describes this situation. Solve by elimination to find the two numbers.


Anyone know???

Answer 1

Call the two numbers x and y

The sum is 82:
x + y = 82
The difference is 24:
x - y = 24

x + y = 82
x - y = 24
Add the two equations to eliminate y:
x + x + y - y = 82 + 24
So
2x = 106
Divide both sides by 2:
x = 53

Substitute back into one of the original equations:
(53) + y = 82
Subtract 53 from both sides:
y = 29

The two numbers are 53 and 29.

Answer 2

Let x and y be those two numbers.
We know that
x + y = 82, and
x - y = 24
So, let's add those two equations in order to eliminate one variable. And we get
x + y + x - y = 82 + 24
2x = 106
x = 106/2 = 53
Subsitute x=53 in one of the two equations. Let's take the first one:
x + y = 82
53 + y = 82
y = 82 - 53
y = 29

Answer: x = 53, y = 29

Answer 3

(1). x+y = 82 & (2). x - y = 24
*Solve for "x' or "y" in either equation - we'll solve for "x" in the 1st equation.

First: subtract "y" from both sides (when you move a term to the opposite side, always use the opposite sign).

(1). x + y = 82
x+y-y = 82-y
x = 82-y

Sec: substitute 82-y with "x" in the 2nd equation.

(2). x - y = 24
82 - y - y = 24
82 - 2y = 24 (subtract 82 from both sides).
82-82-2y = 24-82
- 2y = 24-82
-2y = -58 (divide both sides by -2).
-2y/-2 = -58/-2
y = 58/2
y = 29

Third: substitute 29 with "y" in the 1st equation.

(1). x+y = 82
x+29 = 82 (subtract 29 from both sides).
x+29-29 = 82-29
x = 53

Solution: (53, 29)

Answer 4

let x = first number
y = other number

first equation: x + y = 82

second equation: x - y = 24

express x in terms of y:
x = 82 - y
and
x = 24 + y

eqaute these two
82 - y = 24 + y
-y - y = 24 - 82
y = 29

substitute value of y
x = 82 - 29
x = 53

Answer 5

x+y=82
x-y=24

Sum of the two equations,

2x = 106
x = 53

x+y = 82
53 + y = 82
y = 82 - 53
y = 29

Answer 6

X + Y = 82
X - Y = 24

Add.

2X = 106
X = 53
So Y = 53-24 = 29

Answer 7

x+y=82
x-y=24


x=82-y

82-y-y=24
82-24=2y
58=2y
y=29

x+29=82
x=53

voila, algebraic-ish solution

wow i forgot about just addign the equations together..

I'm an over-achiever!

Answer 8

let no. be x and y
x+y=82
x-y=24
add these together
2x=106
x=53
therefore y=29
therefore the no. are 53 and 29

Answer 9

x + y = 82
x - y = 24-------ADD
2x = 106
x = 53
53 + y = 82
y = 29
x = 53 , y = 29

Answer 10

x + y = 82
x - y = 24