To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied? first equation: 4x − 3y = 34 second equation: 3x 2y = 17

first equation: 4x - 3y = 34

second equation: 3x+2y = 17

To eliminate y, the number before y (coefficient of y ) should be same.

To make the coefficients of y to be same , we multiply the first equation by 2 and second equation by 3

We need to multiply 3y by 2 to get 6y. Also we multiply 2y by 3 to get 6y.

Lets work out and see

first equation: (4x - 3y = 34) * 2

second equation: (3x+2y = 17) * 3

After multiplying each term by constant, The equation becomes

8x - 6y = 68

9x + 6y = 51

17x +0 = 119

17x = 119

x= 7 (we solved for x by eliminating y)

To eliminate y, we multiply the first equation by constant 2 and second equation by constant 3.

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.