Solving a 2x2 system of linear equations

Question

Two systems of equations are given below. For each system choose the best description of its solution. Has no solution, has unqiue solution, or the system has infinitely many solutions.

-3x+y=9

-3x-y=9

The second equation is

4x+y=8

-4x=y+8

Answer 1

First system:

-3x+y=9

-3x-y=9

subtracts the equations: 2y = 0 --> y=0 ---> x=-3, so the solution is (-3,0)

2nd system

4x+y=8

-4x=y+8

Per the second equaiton: 4x = -(y+8)

Substitutes into the first equation:

-(y+8) + y = 8

-y + -8 + y = 8

-8 = 8

NO SOLUTION