Two systems of equations are given below. For each system, choose the best descr

Question

Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. x + 4y = 4 -x - 4y = -4 The system has no solution. The system has a unique solution: (x, y) = () The system has infinitely many solutions. They must satisfy the following equation: y = x + 2y = 8 -x - 2y = 8 The system has no solution. The system has a unique solution: (x, y) = () The system has infinitely many solutions. They must satisfy the following equation: y =

Explanation / Answer

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a)

x + 4y = 4 .........................................(1)

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

Clearly visible from equations above if we multiply equation 2 by scalar -1, then it will result in equation (1).

Hence there cannot be independent solutions to the two system of equations.

The above system of equation shall be thus having infinite solution.

Therefore for each value of x there shall be corresponding values of y

y = (4 - x ) / 4

Solution

b) x + 2y = 8 .............................(1)

- x - 2y = 8 ................................(2)

Clearly while equation (1) sttes that x + 2y is equivalent to value 8 while equation (2) states x + 2y is equivalent to -8.

Hence the system of equations are inconsistent and there shall be no particular solution to the given equation.

Solution

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