# How do you solve the system of equations algebraically #2x-2y+3z=6, 2x-3y+7z=-1, 4x-3y+2z=0#?

##### 1 Answer

There are no solutions

#### Explanation:

The system is presented as thus:

(A)

(B)

(C)

We will pick two pairs of equatwins in the system, and use addition and subtraction to eliminate the same variable from both pairs. We will use A and B, and B and C, for this, eliminating x:

Note that the variable portion of B* is a multiple of the same section in A*, i.e. * by 3 makes the right hand side of the equathin the same as that of B*, then there are infinitely many solutions. If they are unequal, there is no solution. To demonstrate, we try to solve the same as above, using 3A* - B*

3A*-B*

Solutions will,only be present if 0 = 19. Because this is not the case, there are no solutions.