Respuesta :
Answer:
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
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
[tex]y = \frac{25}{3}[/tex]
Substitute [tex]y = \frac{25}{3}[/tex] and z = -3 in equation(i) we will get
x+y+z =10
[tex]x + \frac{25}{3} -3 = 10[/tex]
[tex]x +\frac{25-9}{3} = 10[/tex]
[tex]x +\frac{16}{3} = 10[/tex]
[tex]x = 10 - \frac{16}{3}[/tex]
[tex]x = \frac{30 -16}{3} = \frac{14}{3}[/tex]
Final answer :-
[tex]x =\frac{14}{3} , y = \frac{25}{3} and z = -3[/tex]
The numbers are [tex]-3 ,\frac{14}{3} , \frac{25}{3}[/tex]
Answer:
-2, 5, 7 on Edge.
Step-by-step explanation:
I got the Answer right.
