The sum of two numbers is 82. Their difference is 24. Choose the system of equations that describes this situation. Solve by elimination to find the two numbers.
x+y = 82
x-y = 24
add them
2x = 106
x = 53
in #1
53 + y =82
y = 29
The sum of two numbers is 82. Their difference is 24. Choose the system of equations that describes this situation. Solve by elimination to find the two numbers.
Let's define two variables, x and y, to represent the two numbers.
Based on the given information, we can create the following system of equations:
Equation 1: x + y = 82
Equation 2: x - y = 24
To solve this system using the elimination method, we'll eliminate one variable by adding or subtracting the equations. The goal is to obtain an equation with only one variable that we can solve for.
To eliminate the y variable, we'll multiply Equation 2 by -1 and then add it to Equation 1.
Equation 1: x + y = 82
Equation 2: -x + y = -24
Adding both equations, we get:
( x + y) + ( -x + y) = 82 + ( -24)
x + y - x + y = 82 - 24
2y = 58
Divide both sides of the equation by 2 to solve for y:
2y/2 = 58/2
y = 29
Now that we have the value of y, we can substitute it back into either of the two original equations to solve for x. Let's use Equation 1:
x + y = 82
x + 29 = 82
Subtract 29 from both sides to isolate x:
x + 29 - 29 = 82 - 29
x = 53
Therefore, the two numbers are 53 and 29.
To choose the system of equations that describes this situation, let's define two unknown numbers. Let's call them "x" and "y".
Based on the given information, we have two pieces of information to create two equations:
1. The sum of two numbers is 82. This can be written as: x + y = 82
2. The difference between two numbers is 24. This can be written as: x - y = 24
So, the system of equations that describes this situation is:
x + y = 82
x - y = 24
Now, we can solve this system using the elimination method.
To eliminate the "y" variable, we will add the two equations together:
(x + y) + (x - y) = 82 + 24
2x = 106
Next, we can solve for "x" by dividing both sides of the equation by 2:
2x/2 = 106/2
x = 53
Now that we know the value of "x", we can substitute it back into one of the original equations to find the value of "y". Let's use the first equation:
x + y = 82
53 + y = 82
Subtract 53 from both sides:
y = 82 - 53
y = 29
Therefore, the two numbers are 53 and 29.