Solve by matrix 2c+4p+2b=34, c+3p+b=22 , 3c+2b=17

9514 1404 393

  (c, p, b) = (3, 5, 4)

Step-by-step explanation:

A matrix solver is useful for this purpose. Most graphing calculators will do this, as will a number of web sites. Attached is the output from math software that also solves the matrix equation easily.

The solution is (c, p, b) = (3, 5, 4).

_____

The augmented matrix for the given set of equations is ...

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.