Question

The sum of three numbers is 10. Two times the second number minus the first number is equal to 12

The first number minus the second number plus twice the third number equals 7. Find the numbers.
Listed in order from smallest to largest, the numbers are_
, and_

Answer 1

x = -2, y = 5 and z = 7 in that order

Explanation:

first number = x

second number = y

third number = z

Process

1.- Write equations to solve this problem

x + y + z = 10 Equation l

2y - x = 12 Equation ll

x - y + 2z = 7 Equation lll

2.- Solve equation ll for x

x = 2y - 12

3.- Substitute the previous equation in equation l and lll

(2y - 12) + y + z = 10 (2y - 12) - y + 2z = 7

2y - 12 + y + z = 10 2y - 12 - y + 2z = 7

3y + z = 10 + 12 y + 2z = 19

3y + z = 22

4.- Solve for y and z

-2(3y + z = 22)

y + 2z = 19

-6y - 2z = -44

y + 2z = 19

-5y + 0 = -25

y = -25/-5

y = 5

-Find z

5 + 2z = 19

2z = 19 - 5

2z = 14

z = 14/2

z = 7

5.- Find x

x + 5 + 7 = 10

x = 10 - 5 - 7

x = -2