Solve the system of linear equations by substitution.

−x−8=−y
9y−12+3x=0

The solution is ( , )

The solution (x, y) = (-5, 3)

Step-by-step explanation:

-x - 8 = -y (1)

9y - 12 + 3x = 0 (2)

from equation (1)

-x = - y + 8 ... (3)

multiply equation (3) by -1

x = y - 8 (4)

substituting equation (4) in equation (2)

9y - 12 + 3 ( y - 8) = 0

9y - 12 + 3y - 24 = 0

12y - 36 = 0

12y = 36

y = 36 /12

y = 3

Substitute y = 3 in equation (4)

x = y - 8

x = 3 - 8

x = -5

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

answer is 12345678900987654321234567890987654321

step-by-step explanation: