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 .

The numbers are    

Step-by-step explanation:

Step(i):-

Given sum of the three numbers is 10

Let x , y , z be the three numbers is 10

x +y + z = 10  ...(i)

Given two times the second number minus the first number is equal to 12

2 × y - x = 12 ...(ii)

Given the first number minus the second number plus twice the third number equals 7

x + y + 2 z = 7 ...(iii)

Step(ii):-

Solving (i) and (iii) equations

                       x + y +   z     =    10  ...(i)

                       x + y + 2 z   =     7 ..   (iii)

                     -      -     -         -              

                     0    0    -z      =   3              

Now we know that    z = -3 ...(a)

from (ii)  equation

           2 × y - x = 12 ...(ii)

               x = 2 y -12  ...(b)

Step(iii):-

substitute equations (a) and (b) in equation (i)

                x+y+z =10

           2 y - 12 + y -3 =10

              3 y -15 =10

              3 y = 10 +15

              3 y =25

Substitute    and   z = -3 in equation(i) we will get

        x+y+z =10

Final answer :-

The numbers are  

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)