Two systems of equations are given. Choose the best description of its solution. if applicable, give the solution.

Question

System A

x-3y=-9

-x+3y=9

1. The system has no solution.
2. The system has a unique solution: (x,y) = ( , )
3. The system has infinitely many solutions. They must satisfy the following equation:

y=

System B

x-4y=8

-x+4y=8

1. The system has no solution.
2. The system has a unique solution: (x,y) = ( , )
3. The system has infinitely many solutions. They must satisfy the following equation:

y=

Answer 1

x-3y=-9

-x+3y=9

EQ1: x+9 = 3y

x/3 +3 = y

EQ2: 3y = x+9

y = x/3 + 3

Both equations are the same. It has an infinite number of solutions that satisfy y = x/3 + 3

x-4y=8

-x+4y=8

EQ 1: x-8 = 4y

x/4 - 2 = y

EQ 2: 4y = x+8

y = x/4 + 2

The slopes are the same, but the y intercepts are different. This system has no solutions.