The larger of two numbers is two less than twice the smaller number. The sum of the numbers is 58. Set up a system to find the numbers.

Answer 1

x+y = 58

x-2y = -2

subtract (change the sign of 2nd equation & add is the same as subtraction)

3y = 60

y=20

x=38

Answer 2

larger number = x

smaller number= y

sum = 58

x = 2y - 2

x + y = 58

use substitution method

replace x in second equation with first equation and solve for y

2y - 2 + y = 58

+2. + 2

2y + y = 60

3y = 60

Divide

3y/3 = 60/3

y = 20

Now that we found y we must find x by inserting y in first equation above

x = 2(20) - 2

x = 40 - 2

x = 38

Now insert both numbers into both equations above

x = 2y - 2 x + y = 58

38 = 2(20) - 2 38 + 20 = 58

38 = 40 - 2

38 = 38

Final answer

x= 38

y = 20