The sum of two numbers is 121 and the difference is 27. What are the two
numbers?​

Problem 6: The product of two consecutive odd integers is equal to 675. Find the two integers.

Let x, x + 2 be the two integers. Their product is equak to 144

x (x + 2) = 675

Expand to obtain a quadratic equation.

x 2 + 2 x - 675 = 0

Solve for x to obtain two solutions

x = 25 or x = -27

if x = 25 then x + 2 = 27

if x = -27 then x + 2 = -25

We have two solutions. The two numbers are either

25 and 27

or

-27 and -25

Check that in both cases the product is equal to 675.

not sure

Step-by-step explanation:

The two number are 74 and 47

Step-by-step explanation:

Let the numbers be x and y

x+y=121 and x-y=27

Add the two equation to each other it will be

x+x=2x, y+-y=0, 121+27=148

2x=148 divide both sides by 2

x=74  

Then substitute x with 74 in any of the equations lets say

74+y=121 so y=47

add an image

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1