Chapter 11.1, Problem 29AYU

To determine

To find: The solution of the given system of equations.

Answer to Problem 29AYU

Solution:

Consistent; infinitely many solutions.

Explanation of Solution

Given:

  $x+2y=4$

  $2x+4y=8$

Calculation:

The system of equations is:

  $x+2y=4$

  $2x+4y=8$

Multiplying the first equation by 2 we get,

  $2(x+2y)=2(4)$

  $2x+4y=8,$ which is identical to the second equation.Thus both the equations are coincident and is equal to the equation $2x+4y=8$ .

Hence the given system of equations is consistent and has infinitely many solutions.