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

Answer 1

-10,1,19

Explanation:

x+y+z = 10 (Equation 1)

2y-x= 12 (Equation 2)

x-y+2z = 7 (Equation 3)

(Equation 2): -x = -2y+12

x = 2y-12 (Equation 4)

(Equation 1) - (Equation 3): 2y-z = 3

-z = -2y+3

z = 2y-3 (Equation 5)

Substitute (4) and (5) into (1)

x+y+z = 10

(2y-12)+y+(2y-3) = 10

5y-15 = 10

5y = 5

y=1

Substitute y=1 into (2)

2y-x= 12

2(1)-x= 12

2-x= 12

-x= 12-2

-x= 10

x= -10

Substitute y=1 and x=-10 into (1)

x+y+z = 10

-10+1+z = 10

z-9 = 10

z = 10+9

z = 19

Order: x = -10, y = 1, and z = 19

Answer 2

-2 5 7

Explanation: