Two systems of equations are given below For each system cho

Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. x-2y = 4 The system has no solution.The system has a unique solution: x+2y = 4 =, xy, The system has infinitely many solutions.They must satisfy the following equation: x+3y = 3 The system has no solution.The system has a unique solution: x-3y = 3 , The system has infinitely many solutions.

Solution

First system:

x-2y = 4 .... (1)

-x + 2y = 4

Multiplying this both sides by -1,

x - 2y = -4 ...(2)

From (1) and (2),

4 = -4, which is false forever.

So the given system has no solution.

Second system:

-x + 3y = 3 ... (1)

x - 3y = -3

Multiplying this both sides by -1,

-x + 3y = 3 ...(2)

Both (1) and (2) represent same equation.

So we have two unknown variables with just 1 equation.

So the given system has infinitely many solutions.