Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 4x − y = −5 12x − 3y = 15 one and only one solution infinitely many solutions no solution find the solution, if one exists. (if there are infinitely many solutions, express x and y in terms of the parameter t. if there is no solution, enter no solution.) (x, y) =

NO SOLUTION.

Step-by-step explanation:

4x - y    =  -5

12x - 3y  = 15

Multiply the first equation by 3:

12x - 3y = -15

Note that the left side of this equation is the same as the left side of the second one, but the right sides are different.  The left side cannot be equal to 2 different values. Therefore there  is NO SOLUTION.

Note if we subtract the last 2 equations we get:

0 = 30  which is, of course, absurd.

bru

step-by-step explanation:

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0