Question

The sum of two numbers is 82. Their difference is 34. Write a system of equationsthat describes this situation. Solve by elimination to find the two numbers.O 1) * - y = 82x + y = 3457 and 252) x + y = 82x - y = 3458 and 243)x + y = 82x - y = 3453 and 194) * + y = 34Y - x = 8253 and 25

Answer 1

if x and y are the numbers, then you have the following system of equations:

x + y = 82

x - y = 34

in order to solve the previous system, proceed as follow:

add the equations:

x + y = 82

x - y = 34

2x = 116

divide by 2 the previous equation to obtain x:

x = 116/2

x = 58

next, replace the previous value of x into any of the equation os the system, and solve for y:

x + y = 82

58 + y = 82

subtract 58 both sides:

y = 82 - 58

y = 24

Hence, the solution of the system of equations is

x = 58

y = 24